Search

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations. [ABSTRACT FROM AUTHOR]

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications. [ABSTRACT FROM AUTHOR]

The recently reported compactified hyperboloidal method has found wide use in the numerical computation of quasinormal modes, with implications for fields as diverse as gravitational physics and optics. We extend this intrinsically relativistic method into the non-relativistic domain, demonstrating its use to calculate the quasinormal modes of the Schrodinger equation and solve related bound-state problems. We also describe how to further generalize this method, offering a perspective on the importance of non-relativistic quasinormal modes for the programme of black hole spectroscopy. [ABSTRACT FROM AUTHOR]

In this study, we investigate the dynamics of the Universe during the observed late-time acceleration phase within the framework of the Weyl-type f (Q , T) theory. Specifically, we consider a well-motivated model with the functional form f (Q , T) = α Q + β 6 κ 2 T , where Q represents the scalar of non-metricity and T denotes the trace of the energy–momentum tensor. In this context, the non-metricity Q μ α β of the space-time is established by the vector field w μ . The parameters α and β govern the gravitational field and its interaction with the matter content of the Universe. By considering the case of dust matter, we obtain exact solutions for the field equations and observe that the Hubble parameter H (z) follows a power-law behavior with respect to redshift z. To constrain the model parameters, we analyze various datasets including the Hubble, Pantheon datasets, and their combination. Our results indicate that the Weyl-type f (Q , T) theory offers a viable alternative to explain the observed late-time acceleration of the Universe avoiding the use of dark energy. [ABSTRACT FROM AUTHOR]

A black hole is a mysterious cosmic object that cannot be observed directly, and research on its structure continues with increasing interest today. Investigating the effects on the motion of a half-spin relativistic particle around a black hole may provide us with interesting information. Research on the particle scale requires considering quantum contributions, but a well-established quantum gravity theory has not yet been constructed in literature. In our research, the interaction between the spin of a Dirac particle and the gravitational field is discussed within the scope of the rainbow formalism, which is one of the most studied quantum gravity approaches. [ABSTRACT FROM AUTHOR]

This text discusses the behavior of solutions and the energy stability within Schwarzschild spacetimes, with a particular emphasis on the behavior of massless scalar fields under the influence of a non-rotating and spherically symmetric black hole. The stability of solutions in the proximity of the event horizon of black holes in general relativity remains an open question, especially given the difficulties introduced by minor perturbations that may resemble Kerr solutions. To address this, this work explores a simplified model, including massless scalar fields, to better understand perturbation behaviors around black holes under the Schwarzschild approach. We depart from Richard Price's work in connection with how scalar, electromagnetic, and gravitational fields behave. The tortoise coordinate transformation is considered to set the stage for numerical solutions to the wave equations. Afterward, we explore energy estimates, which are used to gauge stability and wave behavior over time. Our analysis reveals that the time evolution of the energy does not exceed twice its initial value. Further and under the assumption of initial conditions in L2-spaces, we obtain an exponential decreasing behavior in the energy time evolution. A question to continue exploring is how perturbations in L2 in the initial conditions that introduce Kerr solutions as a second-order effect in the linearized equations perturb this obtained exponential decay. [ABSTRACT FROM AUTHOR]

AbstractWe explore the application of Lie symmetries to simplify the gravitational field equations of inhomogeneous cosmology. By employing these symmetries, we demonstrate the construction of a point-like Lagrangian and establish the existence of a minisuperspace description. Finally we show how the Lie symmetries can be applied to construct new solutions for the Wheeler-DeWitt equation. [ABSTRACT FROM AUTHOR]

Surface movement exploration techniques are an important approach to further the understanding of small celestial bodies. Hopping movement is employed to take advantage of the weak gravitational field of small celestial bodies, facilitating long-distance mobility of the rover. The rover exhibits a strong attitude-orbit coupling characteristic during the hopping movement. Different contact attitudes contribute to the challenge of determining the rebound trajectory, rendering it difficult for the rover to maintain continuous movement towards the target position along the nominal trajectory. In this paper, a dual-stage control method for continuous surface hopping movement is developed, wherein the control is applied separately during the flight stage and the collision stage. During the flight stage, applying attitude control enables the rover to establish contact with the surface in a specific attitude, ensuring accuracy in movement direction and creating favorable conditions for the control process in the collision stage. The flywheel is controlled in the collision stage to correct the state change and energy loss due to the collision, enabling the rover to attain the desired hopping state. Considering the energy consumption of the rover, the minimum hopping velocity sequence and angular velocity sequence are designed based on the hopping angle and heading angle. The intricacies and uncertainties inherent in the surface environment of small celestial bodies pose challenges for the rover during hopping and flying. In response to the issue, a finite-time adaptive sliding-mode control law is devised. The control law facilitates the rapid adjustment of the rover to the target attitude in flight, demonstrating strong robustness. In addition, by integrating the changes in contact point velocity with the impulse contact model, the accuracy of the rover's rebound state updates is enhanced. Finally, a set of simulations is performed, and simulation results indicate that the dual-stage control method can achieve a final landing position error of less than 0.2 m for a continuously hopping. The finite-time adaptive sliding-mode control law can stabilize the rover's attitude within 10 s. Conducting 500 Monte Carlo simulations of the continuously hopping rover in three small celestial body surface simulation environments shows that the position endpoint error is within 0.3 m. • An innovative control method for continuous hopping on the surface of small celestial bodies with low gravity is proposed. • The attitude-orbit coupling challenge is addressed through a staged control. • A sequence of hopping states with minimum velocities is devised. • A finite-time adaptive sliding-mode control law is designed to effectively address unknown disturbances. • A corrected sliding-mode control law is developed for precise hopping state updates. [ABSTRACT FROM AUTHOR]

This article explores the complexities surrounding the definition of weight in physics education. It argues that current definitions of weight in pedagogical and metrological literature are unsatisfactory. The article examines weight as a local phenomenon that varies with the location and motion of the reference frame, as well as the forces and interactions involved. It discusses different definitions of weight, the concept of weightlessness, and emphasizes that weight is not an inherent characteristic of an object but depends on nongravitational forces. The article proposes a comprehensive definition of weight that considers all gravitational forces and the local centrifugal force due to celestial object rotation. Examples of weightlessness are provided, such as objects in free fall and astronauts in space. The author, Eugene Hecht, is an emeritus professor of physics with a background in optics, quantum mechanics, and college physics. [Extracted from the article]

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, 〈xμ〉, becomes uncertain. There exists a specific range of coordinates where the accessibility to 〈(xμ)2〉 is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value 〈xμ〉. This expectation value is dependent on 〈(xμ)2〉, which is itself limited by a minimum measurable length Δxmin2. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between Δxmin and −〈g〉μν is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between Δxmin and the Planck length ℓp is established with a proportionality factor of −〈g〉μνβ2, where β2 denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction ψ(x,t), leading to an unrealistic Δp. It is also noted that the lower limit of 〈(pμ)2〉 is directly proportional to the fundamental tensor. [ABSTRACT FROM AUTHOR]

Einstein's expression 'Drama of Ideas' to describe the history of fundamental physics is especially suitable for the problem of quantum gravity (QG). The problem was identified by Einstein in 1916 based on an empirico-cosmological argument that was cosmologically flawed and empirically immeasurable. In 1929, the problem was strikingly underestimated by prominent figures in quantum theory, W. Heisenberg and W. Pauli. In 1929, Bohr, basing on the puzzling results of recent nuclear experiments and theoretical quantum limitations, hypothesized that the law of conservation of energy does not hold in nuclear physics. The young Russian physicist Landau enthusiastically supported Bohr's 'beautiful idea' and in 1931 proposed its theoretical justification, which, however, was rejected by Bohr. In late 1932, Landau realized that Bohr's hypothesis was incompatible with Einstein's theory of gravity. This meeting of two fundamental theories prompted Matvei Bronstein to investigate the quantization of gravity in-depth. In 1935, he proposed the first physical theory of QG for the weak gravity and revealed how deep the QG problem was for strong gravity. He showed that the gravitational field at a point in space–time is in principle unobservable and concluded that a complete theory of QG would require the 'rejection of a Riemannian geometry... and perhaps also the rejection of our ordinary concepts of space and time, replacing them by some much deeper and non-evident concepts'. Until now, despite thousands of publications on QG, the problem remains a great challenge in theoretical physics. [ABSTRACT FROM AUTHOR]

A novel axially symmetric metric is proposed to solve the Einstein field equations. This provides an analytical solution within the matter in the equatorial plane for any galaxy density profile. The solution predicts the observed increase in rotational velocity up to the edge of the galaxy's bulge. However, beyond the bulge, the rotational velocity remains constant, which contradicts the observed peak curves. The existence of the Universe is then considered by approximating the gravitational fields within the galaxy as the sum of those generated by the galaxy and the Universe. The resulting solution explicitly includes a Universe frame-dragging term, aligning with the sixth version of Mach's principle proposed by Bondi and Samuel: "inertial mass is affected by the global distribution of matter". Neglecting the presence of the Universe, stars only have a relative rotation to the bulge, and their rotational velocities monotonically increase with the radial distance r to balance the increasing mass contained in distances < r. At larger distances, the bulge's attraction and its frame-dragging effect decrease, resulting in a constant rotational velocity. When the Universe is considered, stars also have a relative rotation to the non-rotating Universe and experience an additional centrifugal force at any distance from the bulge. This component induces a decrease in rotational velocity as the gravitational influence of the bulge diminishes with r. This model predicts the observed rotational velocity curves for the galaxies M31, M101, and M81 without requiring any dark matter halo or adjustable parameters. This success substantiates Mach's idea as an alternative to the dark matter halo theory. [ABSTRACT FROM AUTHOR]

In this study, the geometrically deformed compact objects in the f(Q, T) gravity theory under an electric field through gravitational decoupling via minimal geometric deformation (MGD) technique are developed for the first time. The decoupled field equations are solved via two different mimic approaches Θ00=ρ${\Theta}_{0}^{0}=\rho $ and Θ11=pr${\Theta}_{1}^{1}={p}_{r}$ through the Karmarkar condition. Physical viability tests are conducted on our models and examine how decoupling parameters affect the physical qualities of objects. The obtained models are compared with the observational constraints for neutron stars PSR J1810+174, PSR J1959+2048, and PSR J2215+5135, including GW190814. Particularly, by modifying parameters α and n, the occurrence of a “mass gap” component is accomplished. The resulting models exhibit stable, well‐behaved mass profiles, regular behavior and no gravitational collapse, as verified by the Buchdahl–Andréasson's limit. Furthermore, a thorough physical analysis that is based on two parameters: n (f(Q, T)–coupling parameter) and α (decoupling parameter) is provided. This work extends our current understanding of compact star configurations and sheds light on the behavior of compact objects in the f(Q, T) gravity. [ABSTRACT FROM AUTHOR]

A gravitational field can cause a rotation of the polarisation vector of light. This phenomenon is known as the gravitational Faraday effect. We study the gravitational Faraday effect of linearly polarised light propagating in the gravitational field of a weak plane gravitational wave (GW) with " + ", " × ", and elliptical polarisation modes. The corresponding gravitational Faraday rotation angle is proportional to the GW amplitude and to the squared distance traveled by the light and inversely proportional to the GW squared wavelength. The Faraday rotation is maximal if the light propagates along directions perpendicular to the GW propagation and tilted by π / 4 to the directions of its polarisation. There is no a gravitational Faraday rotation when light and a GW propagate along the same directions, or when light propagates along directions of a GW polarisation. Helicity of an elliptically polarised GW gives cubic order contribution to the Faraday rotation. [ABSTRACT FROM AUTHOR]

This paper presents a general strategy for tracking the scale-span movement process of asteroid regolith materials. It achieves the tracking of the mass movement on the asteroid at a realistic scale, under conditions of high-resolution asteroid surface topography (submeter level) and actual regolith particle sizes. To overcome the memory exponential expansion caused by the enlarged computational domain, we improved the conventional cell-linked list method so that it can be applied to arbitrarily large computational domains around asteroids. An efficient contact detection algorithm for particles and polyhedral shape models of asteroids is presented, which avoids traversing all surface triangles and thus allows us to model high-resolution surface topography. A parallel algorithm based on Compute Unified Device Architecture for the gravitational field of the asteroid is presented. Leveraging heterogeneous computing features, further architectural optimization overlaps computations of the long-range and short-range interactions, resulting in an approaching doubling of computational efficiency compared to the code lacking architectural optimizations. Using the above strategy, a specific high-fidelity discrete element method code that integrates key mechanical models, including the irregular gravitational field, the interparticle and particle-surface interactions, and the coupled dynamics between the particles and the asteroid, is developed to track the asteroid regolith mass movement. As tests, we simulated the landslide of a sand pile on the asteroid's surface during spin-up. The simulation results demonstrate that the code can track the mass movement of the regolith particles on the surface of the asteroid from local landslides to mass leakage with good accuracy. [ABSTRACT FROM AUTHOR]

The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of O 1 , the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle. [ABSTRACT FROM AUTHOR]

We consider a dynamic scenario for characterizing the late Universe evolution, aiming to mitigate the Hubble tension. Specifically, we consider a metric f (R) gravity in the Jordan frame which is implemented to the dynamics of a flat isotropic Universe. This cosmological model incorporates a matter creation process, due to the time variation of the cosmological gravitational field. We model particle creation by representing the isotropic Universe (specifically, a given fiducial volume) as an open thermodynamic system. The resulting dynamical model involves four unknowns: the Hubble parameter, the non-minimally coupled scalar field, its potential, and the energy density of the matter component. We impose suitable conditions to derive a closed system for these functions of the redshift. In this model, the vacuum energy density of the present Universe is determined by the scalar field potential, in line with the modified gravity scenario. Hence, we construct a viable model, determining the form of the f (R) theory a posteriori and appropriately constraining the phenomenological parameters of the matter creation process to eliminate tachyon modes. Finally, by analyzing the allowed parameter space, we demonstrate that the Planck evolution of the Hubble parameter can be reconciled with the late Universe dynamics, thus alleviating the Hubble tension. [ABSTRACT FROM AUTHOR]

High power output and high conversion efficiency are crucial parameters for microbial fuel cells (MFCs). In our previous work, we worked with microfluidic MFCs to study fundamentals related to the power density of the MFCs, but nutrient consumption was limited to one side of the microchannel (the electrode layer) due to diffusion limitations. In this work, long-term experiments were conducted on a new four-electrode microfluidic MFC design, which grew Geobacter sulfurreducens biofilms on upward- and downward-facing electrodes in the microchannel. To our knowledge, this is the first study comparing electroactive biofilm (EAB) growth experiencing the influence of opposing gravitational fields. It was discovered that inoculation and growth of the EAB did not proceed as fast at the downward-facing anode, which we hypothesize to be due to gravity effects that negatively impacted bacterial settling on that surface. Rotating the device during the growth phase resulted in uniform and strong outputs from both sides, yielding individual power densities of 4.03 and 4.13 W m−2, which increased to nearly double when the top- and bottom-side electrodes were operated in parallel as a single four-electrode MFC. Similarly, acetate consumption could be doubled with the four electrodes operated in parallel. [ABSTRACT FROM AUTHOR]

In this study, our primary focus lies in meticulously exploring the intricacies of the universe by employing a flat Friedmann–Lemaître–Robertson–Walker (FLRW) model within the framework of f(R,G) gravity. In our analysis, the f(R,G) function is delineated as the sum of two distinct components, commencing with a quadratic correction of the geometric term denoted by f(R), structured as f(R) = R + ξR2, alongside a matter term denoted by f(G) = λG2, where R and G symbolize the Ricci scalar and Gauss–Bonnet invariant, respectively. In the pursuit of solutions to the gravitational field equations within the f(R,G) formalism, we embrace a specific expression for the scale factor, represented as a =sinh 1 α(βt) [D. Rabha and R. R. Baruah, The dynamics of a hyperbolic solution in f(R,G) gravity, Astron. Comput. 45 (2023) 100761]. In this context, the parameters α and β intricately shape the scale factor’s behavior. The model posits the intriguing prospect of perpetual cosmic acceleration when 0 < α < 1.19, signifying a continuous expansion of the universe. Conversely, for α ≥ 1.19, the model proposes a pivotal transition from an early deceleration phase to the present accelerated epoch, a transformative shift in line with our understanding of cosmic evolution. Furthermore, the model demonstrates its credibility by satisfying Jean’s instability condition during the shift from a radiation-dominated era to a matter-dominated era, substantiating the formation of cosmic structures. In our analysis, a central focus is directed toward scrutinizing the equation of state parameter ω within our model. We delve into a comprehensive examination of the scalar field and meticulously assess the energy conditions surrounding the derived solution. To establish the robustness of our model, we deploy an array of diagnostic tools, including the Jerk, Snap, and Lerk parameters, along with the Om diagnostic, Classical stability of the model, and statefinder diagnostic tools, Observational Constraints on the Model Parameters. The outcomes, intertwined with a detailed analysis of both the results and the inherent intricacies of the model, are diligently clarified and presented. [ABSTRACT FROM AUTHOR]

The paper aims to apply the trigintaduonion spaces to explore the physical properties of four interactions simultaneously, including the electromagnetic fields, gravitational fields, weak nuclear fields, and strong nuclear fields. J. C. Maxwell first applied the algebra of quaternions to study the physical properties of electromagnetic fields. It inspired some subsequent scholars to introduce the quaternions, octonions, sedenions, and trigintaduonions to research the electromagnetic fields, gravitational fields, weak nuclear fields, strong nuclear fields, quantum mechanics, gauge fields, and curved spaces and so forth. The algebra of trigintaduonions is able to discuss the physical quantities of four interactions, including the field potential, field strength, field source, linear momentum, angular momentum, torque, and force. In the field theories described with the algebra of trigintaduonions, the weak nuclear field is composed of three types of fundamental fields. These three fundamental fields, related to weak nuclear fields, can describe the physical properties of weak nuclear fields collectively. This is consistent with the conclusion of the electroweak theory. Meanwhile the strong nuclear field consists of three types of fundamental fields. These three fundamental fields relevant to strong nuclear fields may investigate the physical properties of strong nuclear fields mutually. It is coincident with the deduction of quark theory. According to the properties of trigintaduonions, one can deduce the Yang‐Mills equation related to the gauge fields. It means that the electromagnetic field occupies a quaternion space. The gravitational field owns one different quaternion space. The weak nuclear fields occupy three mutually independent quaternion spaces. The properties of weak nuclear fields are different from those of electromagnetic fields or gravitational fields. According to the multiplication table of trigintaduonion spaces, the strong nuclear fields own three conjugate quaternion spaces independent of each other. These explorations further deepen the understanding of the physical properties of weak and strong nuclear fields. [ABSTRACT FROM AUTHOR]

Context. Flat rotation curves, v(r), are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Aims. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. Methods. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. Results. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way's DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Conclusions. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar. [ABSTRACT FROM AUTHOR]

Microlensing of stars in strongly lensed galaxies can lead to temporary extreme magnification factors (μ> 1000), enabling their detection at high redshifts. Following the discovery of Icarus, several stars at cosmological distances (z > 1) have been observed using the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). This emerging field of gravitational lensing holds promise to study individual high redshift stars. It also offers the opportunity to study the substructure in the lens plane with implications for dark matter models, as more lensed stars are detected and analysed statistically. Due to the computational demands of simulating microlensing at large magnification factors, it is important to develop fast and accurate analytical approximations for the probability of magnification in such extreme scenarios. In this study, we consider different macro-model magnification and microlensing surface mass density scenarios and study how the probability of extreme magnification factors depends on these factors. To achieve this, we created state-of-the-art large simulations of the microlensing effect in these scenarios. Through the analysis of these simulations, we derived analytical scaling relationships that can bypass the need for expensive numerical simulations. Our results are useful to interpret current observations of stars at cosmic distances which are extremely magnified and under the influence of microlenses. [ABSTRACT FROM AUTHOR]

In this study, we explore the quantum effects in the Schwarzschild spacetime for massive and massless scalar particles in the presence of an external gravitational field. The methodology involves the analytical solution of the Klein–Gordon equation for the scalar particles in the near-horizon spacetime limit, using Rindler approximation. The results show that the quantum effects differ significantly for the massive and massless cases, they possess similar characteristics near the event horizon. Bosons without mass that are distant from the event horizon undergo a reduced gravitational impact and possess a symmetric wave function that remains unchanged when they approach the event horizon. However, the symmetry is lost, indicating that the particle strives for a lower energy state and becomes erratic as it nears the event horizon. This aligns with the anticipated behavior of particles within the Schwarzschild horizon. The particles have an energy spectrum even for tremendous values of the Schwarzschild radius, which entails the validity of the Rindler approximation in the near horizon geometry. We have observed that the quantum effects of massive and massless particles differ based on the mass. Specifically, massive and massless scalars behave differently due to their geometric differences, which results in different eigenstates. Although they both tend to seek lower energy levels when they approach the event horizon, their behavior is not the same. [ABSTRACT FROM AUTHOR]

The complete title of this paper should be “The geometry of the constant gravitational field or how to switch from the mechanical Lagrangian to a geometric Lagrangian” and in this abstract we sketch why. To begin with, let us say that Einstein managed to integrate the constant gravitational field in the special theory of relativity, obtaining a metric whose geodesics are locally parabolas. The existence of a similar metric deduced from the considerations of Newtonian mechanics is somehow obstructed by the Lagrangian involved in the description of the constant gravitational field. Therefore, we need to explain how the mechanical Lagrangian above which is not suitable for a metric description of the constant gravitational field can be switched into a geometrical Lagrangian having the same geodesics and suitable for the metric description of the constant gravitational field. The geometric method found by us is related to a parabolic type of transformations. A consequence of the previous method can be applied for the study of bending of light rays in a constant gravitational field. [ABSTRACT FROM AUTHOR]

The paper examines the problem of unique determination of the fundamental solution of a mesh analogue of Laplace's equation within the theory of discrete gravitational potential. The mesh fundamental solution of the finite-difference analogue of Laplace's equation plays a key role in reconstructing a continuously distributed source of gravitational or magnetic field from heterogeneous and different-precision data obtained at points of a certain mesh set. [ABSTRACT FROM AUTHOR]

A four-dimensional differential Euler-Lagrange equation for continuously distributed materials is derived based on the principle of least action, and instead of Lagrangian, this equation contains the Lagrangian density. This makes it possible to determine the density of generalized fourmomentum in covariant form as derivative of the Lagrangian density with respect to four-velocity of typical particles of a system taken with opposite sign, and then calculate the generalized fourmomentum itself. It is shown that the generalized four-momentum of all typical particles of a system is an integral four-vector and therefore should be considered as a special type of fourvectors. The presented expression for generalized four-momentum exactly corresponds to the Legendre transformation connecting the Lagrangian and Hamiltonian. The obtained formulas are used to calculate generalized four-momentum of stationary and moving relativistic uniform systems for the Lagrangian with particles and vector fields, including electromagnetic and gravitational fields, acceleration field and pressure field. It turns out that the generalized fourmomentum of a moving system depends on the total mass of particles, on the Lorentz factor and on the velocity of the system's center of momentum. Besides, an additional contribution is made by the scalar potentials of the acceleration field and the pressure field at the center of system. The direction of the generalized four-momentum coincides with the direction of four-velocity of the system under consideration, while the generalized four-momentum is part of the relativistic fourmomentum of the system. [ABSTRACT FROM AUTHOR]

High-accuracy optical clocks have garnered increasing attention for their potential application in various fields, including geodesy. According to the gravitational red-shift effect, clocks at lower altitudes on the Earth's surface run slower than those at higher altitudes due to the differential gravitational field. Consequently, the geopotential difference can be determined by simultaneously comparing the frequency of two optical clocks at disparate locations. Here, we report geopotential difference measurements conducted using a pair of transportable 40Ca+ optical clocks with uncertainties at the 10 − 17 level. After calibrating the output frequencies of two optical clocks in the horizontal position, frequency comparison is realized by moving Clock 2 to two different positions using a high-precision optical fiber time–frequency transmission link with Clock 1. The elevation difference of the two different positions, as processed by ensemble empirical mode decomposition (EEMD), is measured as −88.4 cm ± 16.7 cm and 104.5 cm ± 20.1 cm, respectively, which is consistent with the geometric measurement results within the error range. This experimental result validates the credibility of the optical clock time–frequency comparison used in determining geopotential differences, thereby providing a novel measurement model for the establishment of a global unified elevation datum. [ABSTRACT FROM AUTHOR]

A quantum well (QW) diode that is capable of emitting light is also capable of absorbing light. In particular, the QW diode has broad electroluminescence and responsivity spectra and thus, a distinct spectral overlap exists, enabling the establishment of light communication using two identical QW diodes, namely, one as the transmitter and the other as the receiver. Here, we demonstrate a time-division multiplexing (TDM) wireless light communication using two identical green QW diodes that are defined by software as transmitter or receiver to achieve real-time underwater data transmission via the same optical channel. To further exploit this dual emission-detection characteristics, we unite energy conservation, gravitational field and energy diagram theory to arrive the conclusion that the gravitational field may play a key role in the irreversibility between light emission and detection of the QW diode. [ABSTRACT FROM AUTHOR]

The compressibility effects have been studied on the internal wave modes and Rayleigh-Taylor (R-T) instability in a magnetized strongly coupled dusty plasma (SCDP). A dusty fluid model is constructed considering the effects of weakly coupled electrons/ions and strongly coupled dust grains under the influence of the gravitational field. The effects of the magnetic field and viscoelastic coefficients have been incorporated under the generalized hydrodynamic (GH) fluid description in a quasineutral dusty plasma. The dispersion relation of R-T instability is derived analytically and discussed in the strongly coupled limit. The compressibility effects have appeared in the internal wave modes, significantly modifying the R-T instability criterion and growth rates. The Coulomb coupling parameter and dust magnetosonic speed suppress the growth rate of the R-T instability in a compressible SCDP. [ABSTRACT FROM AUTHOR]

We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity. [ABSTRACT FROM AUTHOR]

The Brillouin sphere is defined as the smallest sphere, centered at the origin of the geocentric coordinate system, that incorporates all the condensed matter composing the planet. The Brillouin sphere touches the Earth at a single point, and the radial line that begins at the origin and passes through that point is called the singular radial line. For about 60 years there has been a persistent anxiety about whether or not a spherical harmonic (SH) expansion of the external gravitational potential, V, will converge beneath the Brillouin sphere. Recently, it was proven that the probability of such convergence is zero. One of these proofs provided an asymptotic relation, called Costin's formula, for the upper bound, EN, on the absolute value of the prediction error, eN, of a SH series model, V N (θ , λ , r) , truncated at some maximum degree, N = n max . When the SH series is restricted to (or projected onto) a particular radial line, it reduces to a Taylor series (TS) in 1 / r . Costin's formula is E N ≃ B N − b (R / r) N , where R is the radius of the Brillouin sphere. This formula depends on two positive parameters: b, which controls the decay of error amplitude as a function of N when r is fixed, and a scale factor B. We show here that Costin's formula derives from a similar asymptotic relation for the upper bound, An on the absolute value of the TS coefficients, an, for the same radial line. This formula, A n ≃ K n − k , depends on degree, n, and two positive parameters, k and K, that are analogous to b and B. We use synthetic planets, for which we can compute the potential, V, and also the radial component of gravitational acceleration, g r = ∂ V / ∂ r , to hundreds of significant digits, to validate both of these asymptotic formulas. Let superscript V refer to asymptotic parameters associated with the coefficients and prediction errors for gravitational potential, and superscript g to the coefficients and predictions errors associated with gr. For polyhedral planets of uniform density we show that b V = k V = 7 / 2 and b g = k g = 5 / 2 almost everywhere. We show that the frequency of oscillation (around zero) of the TS coefficients and the series prediction errors, for a given radial line, is controlled by the geocentric angle, α, between that radial line and the singular radial line. We also derive useful identities connecting K V , B V , K g , and Bg. These identities are expressed in terms of quotients of the various scale factors. The only other quantities involved in these identities are α and R. The phenomenology of 'series divergence' and prediction error (when r < R) can be described as a function of the truncation degree, N, or the depth, d, beneath the Brillouin sphere. For a fixed r ⩽ R , as N increases from very low values, the upper error bound EN shrinks until it reaches its minimum (best) value when N reaches some particular or optimum value, N opt . When N > N opt , prediction error grows as N continues to increase. Eventually, when N ≫ N opt , prediction errors increase exponentially with rising N. If we fix the value of N and allow R / r to vary, then we find that prediction error in free space beneath the Brillouin sphere increases exponentially with depth, d, beneath the Brillouin sphere. Because b g = b V − 1 everywhere, divergence driven prediction error intensifies more rapidly for gr than for V, both in terms of its dependence on N and d. If we fix both N and d, and focus on the 'lateral' variations in prediction error, we observe that divergence and prediction error tend to increase (as does B) as we approach high-amplitude topography. [ABSTRACT FROM AUTHOR]

We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour. [ABSTRACT FROM AUTHOR]

This article explores the implications of bridging quantum mechanics and general relativity when the Unruh effect is observed by a particle moving at escape velocity in a gravitational field. A quantum model is developed where the Unruh effect can produce a graviton particle which when added to the Universe would increase the information content of the Universe horizon by one bit of energy as per the holographic principle. A strange particle, s = 95 MeV/c², can produce a graviton via the Unruh effect in its gravitational field at a distance of its particle wavelength from its center of mass. If the smallest unit of information is one bit, the strange particle would be the smallest detector possible in our Universe, limiting the vacuum energy density to 10-9 J/m³. Observers at the strange particle wavelength would 26 1 observe a Rindler horizon at RH = 2$R = 10 m and would perceive the ratio of matter as -- = 0.309 of the Universe energy. A wavefunction can be used to represent membranes composed of wave packets of strange particle energy and these membranes made up of any quantized number of strange particles can be used to determine the limits of size and structure of mass-energy composition within our Universe along with providing a mechanism for the expansion of the Universe itself. The luminosity of stars, quasars, and galaxies can be predicted by this model. It is theorized that the Universe contains Q quanta of time, Q³ bits of information, and can be modeled with Q² strange particles. Finally, the Unruh effect from a group of Q particles will always stretch space by a strange particle wavelength and produce a new strange particle pair for each quantum of time, equivalent to the strong interaction. [ABSTRACT FROM AUTHOR]

In this contribution, gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion [J. A. S. Gallegos et al., Phys. Rev. E 104, 064606 (2021)], the influence of the gravitational field, characterized by the gravitational Péclet number, Pe, on patchy colloids is studied in terms of the patchy coverage, χ. Our findings point out that there exists a threshold Péclet number, Peg, that depends on χ above which the gravitational field enhances the particle bonding and, in consequence, promotes the aggregation or clustering of particles; the smaller the χ value, the higher the Peg. Interestingly, when χ ∼ 1 (near the isotropic limit), our results are consistent with an experimentally determined threshold Pe value where gravity affects the gel formation in short-range attractive colloids. In addition, our results show that the cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster, i.e., gravity is able to modify the structure of the gel-like states. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure, where an interesting structural scenario emerges, namely, depending on the Pe value, the new heterogeneous gel-like states can coexist with both diluted and dense phases or they simply reach a crystalline-like state. In the isotropic case, the increase in the Pe number can shift the critical temperature to higher temperatures; however, when Pe > 0.01, the binodal disappears and the particles fully sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also note that within the values of the Péclet number here explored, the cluster morphology is barely altered. [ABSTRACT FROM AUTHOR]

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation with quadratic potential. For the initial value problem we establish a global existence theory when initial data are prescribed on a future light cone with vertex at the center of symmetry. A suitably generalized solution in Bondi coordinates is sought which has low regularity and possibly large but finite Bondi mass. A similar result was established first by Christodoulou for massless fields. In order to deal with massive fields, we must overcome several challenges and significantly modify Christodoulou's original method. First of all, we formulate the Einstein-Klein-Gordon system in spherical symmetry as a non-local and nonlinear hyperbolic equation and, by carefully investigating the global dynamical behavior of the massive field, we establish various estimates concerning the Einstein operator, the Hawking mass, and the Bondi mass, including novel positivity and monotonicity properties. Importantly, in addition to a regularization at the center of symmetry we find it necessary to also introduce a regularization at null infinity. We also establish new energy and decay estimates for, both, regularized and generalized solutions. [ABSTRACT FROM AUTHOR]

The estimation of the Hubble constant in the past few decades has increasingly become more accurate with the advancement of new techniques. However, its value seems to depend on the epoch at which the measurements are made. The Planck estimate of the Hubble constant from the observations of the cosmic microwave background radiation in the early universe is about 6 7 km \ s \ Mpc , whereas that obtained from the distance indicators at the current epoch is ∼ 7 3 − 7 4 km \ s \ Mpc. This discrepancy between the two groups of measurement is termed as the Hubble tension which has gained much attention in the past few decades with growing significance as measurements from both, the early and the late universe, studies continue to produce results with increasing precision. In this work, we propose a modification to gravity by considering a finite range gravitational field as an alternate explanation for this discrepancy in the value of the Hubble constant. [ABSTRACT FROM AUTHOR]

Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is mitigated, at least in part. [ABSTRACT FROM AUTHOR]

For polyhedral mass bodies having arbitrary shape and density distribution of polynomial type we present a tensorial approach to derive analytical expressions of the gravitational potential and gravity vector. They are evaluated at an arbitrary point by means of formulas, referred to a Cartesian reference frame having an arbitrary origin, that are shown to be singularity-free whatever is the position of the observation point with respect to the body. The solution is expressed as a sum of algebraic quantities depending solely upon the 3D coordinates of the polyhedron vertices and the coefficients of the polynomial density function. Hence, no recursive expression needs to be invoked as in the recent contribution by Ren et al. (Surv Geophys 41:695–722, 2020). Moreover, the tensorial formalism developed in the paper allows one to obtain more concise, coordinate-free expressions that can also be extended to address polynomial functions of greater order. The analytical expressions of the gravitational potential and gravity vector are numerically validated and compared with alternative methods retrieved from the literature. [ABSTRACT FROM AUTHOR]

Integral transformations represent an important mathematical tool for gravitational field modelling. A basic assumption of integral transformations is the global data coverage, but availability of high-resolution and accurate gravitational data may be restricted. Therefore, we decompose the global integration into two parts: (1) the effect of the near zone calculated by the numerical integration of data within a spherical cap and (2) the effect of the far zone due to data beyond the spherical cap synthesised by harmonic expansions. Theoretical and numerical aspects of this decomposition have frequently been studied for isotropic integral transformations on the sphere, such as Hotine's, Poisson's, and Stokes's integral formulas. In this article, we systematically review the mathematical theory of the far-zone effects for the spherical integral formulas, which transform the disturbing gravitational potential or its purely radial derivatives into observable quantities of the gravitational field, i.e. the disturbing gravitational potential and its radial, horizontal, or mixed derivatives of the first, second, or third order. These formulas are implemented in a MATLAB software and validated in a closed-loop simulation. Selected properties of the harmonic expansions are investigated by examining the behaviour of the truncation error coefficients. The mathematical formulations presented here are indispensable for practical solutions of direct or inverse problems in an accurate gravitational field modelling or when studying statistical properties of integral transformations. [ABSTRACT FROM AUTHOR]

In this article, we investigate the Nordström–Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov–Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a better regularity of weak solutions for the field than the one proved by Calogero and Rein [J. Differ. Equ. 204, 323 (2004)]. Meanwhile, under the additional integrability condition, we establish the energy conservation of the weak solution. [ABSTRACT FROM AUTHOR]

Einsteinian gravity, of which Newtonian gravity is a part, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose. The hypothesis that founds the basis of both Einsteinian and Newtonian theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the Einstein's equations is one of the assumptions that underlies the proof of the singularity theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the same. In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the "large distance" scenario. To mention a specific instance, under the gravity of the earth, a 5 kg and a 500 kg fall with accelerations which differ by approximately 113.148 × 10 - 32 meter/sec 2 and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the "small distance" regime which automatically justifies why the Einstein's and Newton's theories fail to provide any "small distance" analysis. In course of writing down this theory, I demonstrate why the continuum hypothesis as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes' self-skepticism concerning exact representation of numbers by drawing lines (ii) Born's wish of taking into account "natural uncertainty in all observations" while describing "a physical situation" by means of "real numbers" (iii) Klein's vision of having "a fusion of arithmetic and geometry" where "a point is replaced by a small spot" (iv) Goedel's assertion about "non-standard analysis, in some version" being "the analysis of the future". [ABSTRACT FROM AUTHOR]

A magnetic field is generated to modify the effective gravity acting on settling particles in a laboratory experiment. When applied to a magnetized spherical particle settling in water-glycerol mixtures, the magnetic field produces a vertical force that counteracts the gravitational field, hence allowing for the magnetic tuning of the settling properties of the particle. While doing so, the spin of the particle around the direction perpendicular to the applied magnetic field is blocked, thus allowing spin solely around the direction of the magnetic field. This method of magnetic modification of the effective gravity is tested on the settling of spherical magnets in quiescent fluids over Galileo numbers in the range [100, 300] and a fixed particle density of 8200 kg/m 3 . The results obtained by varying the Galileo number via the magnetic modification of effective gravity are compared to those obtained with non-magnetic spheres when the Galileo number is modified by varying the fluid's viscosity. We show that the same taxonomy of settling regimes with nearly identical geometrical properties (in terms of planarity and obliqueness) of the trajectories is recovered. In addition to proving that it is possible to magnetically tame the settling of particles in fluids preserving the features of the non-magnetic case, this also reveals that blocking the spin of the particles does not produce any significant effect on its settling properties in a quiescent fluid. This novel experimental methodology opens new possibilities to experimentally explore many other subtle aspects of the coupling between settling particles and fluids (for instance, to disentangle the effects of rotation, inertia, and/or anisotropy of the particles) in more complex situations including the case of turbulent flows. [ABSTRACT FROM AUTHOR]

The gravity model is a widely recognized tool for estimating the movement of people and goods. In this study, we introduce two gravitational variables, population size and regional GDP per capita (RGDPPC), to explain the characteristics of population movement between and within cities in South Korea. A log-linearized gravity model is employed to run regression analyses at three spatial levels: the national level (encompassing the entirety of South Korea), the metropolitan level (focusing on the Seoul and Busan Metropolitan Transportation Areas) and the city level (specifically in Seoul and Busan). The study incorporates data on various modes of transportation from 246 of the 250 municipalities in South Korea. Predictive performance of the model is better when utilizing national-level data. However, as spatial area decreases and population density increases, the models explanatory power decreases significantly when relying solely on data related to either population size or RGDPPC. The findings suggest that incorporation of both population size and RGDPPC into the gravity model best captures the dynamics of traffic flow within economically integrated regions. This relationship is analogous to gravitational fields generated by two distinct types of mass. Including both population size and RGDPPC, the gravity model can be leveraged effectively to estimate traffic patterns, particularly within regions characterized by high economic integration. [ABSTRACT FROM AUTHOR]

The detection and study of spectral signs of sublimation-driven dust activity (SDA) in 20 primitive-type asteroids of the Main Belt observed in the visible range allowed us to ascertain its temporal (or periodic) character. The asteroids exhibit SDA of relatively low intensity at minimal heliocentric distances, when their subsolar temperatures are, accordingly, highest (i.e., the surface temperature of the asteroid at the center of its sunlit hemisphere is close to the absolute maximum). Most likely, the major cause of SDA in these asteroids is that their interior contains H2O ice, which becomes outcropped due to recent impact events. As follows from the numerical modeling of the reflectance spectra of active asteroids under consideration, the optically thin dust exosphere (DE), which was induced by SDA and envelopes these bodies, consists of submicron homogeneous particles of different composition and/or fractal-like aggregates of such particles. Taking into account an extremely weak gravitational field of asteroids that cannot hold this optically thin DE even for a short time (especially, if their sizes are less than ~10 km), we conclude that the DE of active primitive-type asteroids is supported by two jointly operating mechanisms. Namely, the electrostatic field of photoemission nature creates a plasma–dust sheath on a sunlit side of the asteroid (as in all atmosphereless celestial bodies), and SDA provides the additional ejection of dust particles from the surface into this layer, which enhances their amount to a detectable level; at the same time, the self-rotation of the body contributes to the spreading of dust around the asteroid. [ABSTRACT FROM AUTHOR]

We investigate the response of Casimir energies to fluctuations in a scalar field in the background of a weak gravitational field in κ -deformed space-time. We model the Casimir plates in a gravitational field by κ -deformed Rindler coordinates and calculate the Casimir energy using the κ -deformed scalar field. We show that the Casimir energy accelerates in a weak gravitational field like a mass. Thus, our calculations show that the mass–energy equivalence principle holds in κ -deformed space-time even though a length scale is introduced through space-time non-commutativity. [ABSTRACT FROM AUTHOR]

Linearized differential equations appear in this article in the context of light and particle deflection in Schwarzschild spacetime, the simplest metric solution of Einstein's equations. The procedures can be easily employed in upper level undergraduate courses, and the results illustrate the frequent failure of the Einstein equivalence principle in predicting deflection due to spatial curvature. The full geodesic equations are themselves readily accessible, but they need not necessarily be derived or addressed in order for students to gain an appreciation of the limited validity of equating particle motion in an accelerating Lorentz frame of reference to motion under the influence of Newtonian gravity. We show by direct calculation that the common equivalence principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is, therefore, possible, at least as a matter of principle, to tell the difference between local acceleration and a true gravitational field by measuring the local deflection of light. We calculate as well the deflection of test particles of arbitrary energy and construct a leading-order coordinate transformation from Schwarzschild to local inertial coordinates, which shows explicitly how the effects of spatial curvature manifest locally for relativistic trajectories of both finite and vanishing rest mass particles. [ABSTRACT FROM AUTHOR]