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Aiming at the Terrestrial Water Storage(TWS) changes in the Amazon River basin, this article uses the coordinate time series data of the Global Navigation Satellite System (GNSS), adopts the Variational Mode Decomposition and Bidirectional Long and Short Term Memory(VMD-BiLSTM) method to extract the vertical crustal deformation series, and then adopts the Principal Component Analysis(PCA) method to invert the changes of terrestrial water storage in the Amazon Basin from July 15, 2012 to July 25, 2018. Then, the GNSS inversion results were compared with the equivalent water height retrieved from Gravity Recovery and Climate Experiment (GRACE) data. The results show that (1) the extraction method proposed in this article has better denoising effect than the traditional method; (2) the surface hydrological load deformation can be well calculated using GNSS coordinate vertical time series, and then the regional TWS changes can be inverted, which has a good consistency with the result of GRACE inversion of water storage, and has almost the same seasonal variation characteristics; (3) There is a strong correlation between TWS changes retrieved by GNSS based on surface deformation characteristics and water mass changes calculated by GRACE based on gravitational field changes, but GNSS satellite's all-weather measurement results in a finer time scale compared with GRACE inversion results. In summary, GNSS can be used as a supplementary technology for monitoring terrestrial water storage changes, and can complement the advantages of GRACE technology. [ABSTRACT FROM AUTHOR]

The equation of state of quantum fluctuations of the gravitational field of the universe depends on H 4 , where H is the Hubble constant. This means that it is invariant with respect to the Wick rotation, i.e., the transition from Lorentzian space-time to Euclidean space-time and vice versa. It is shown that the quantum birth of universes from Euclidean space-time, i.e., from nothing, and their quantum disappearance to nothing (return to Euclidean space-time) by the time the density of the matter filling the universe becomes negligible could be a likely cosmological scenario. On an infinite time axis, this is an endless process of birth and death of universes appearing and disappearing and replacing each other. Within this scenario, our current universe is going to disappear into nothing at z ≤ − 0.68 , i.e., after 18.37 billion years, and the lifetime of our universe and similar universes is about 32 billion years. [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]

Gravity forward modeling as a basic tool has been widely used for topography correction and 3D density inversion. The source region is usually discretized into tesseroids (i.e., spherical prisms) to consider the influence of the curvature of planets in global or large-scale problems. Traditional gravity forward modeling methods in spherical coordinates, including the Taylor expansion and Gaussian–Legendre quadrature, are all based on spatial domains, which mostly have low computational efficiency. This study proposes a high-efficiency forward modeling method of gravitational fields in the spherical harmonic domain, in which the gravity anomalies and gradient tensors can be expressed as spherical harmonic synthesis forms of spherical harmonic coefficients of 3D density distribution. A homogeneous spherical shell model is used to test its effectiveness compared with traditional spatial domain methods. It demonstrates that the computational efficiency of the proposed spherical harmonic domain method is improved by four orders of magnitude with a similar level of computational accuracy compared with the optimized 3D GLQ method. The test also shows that the computational time of the proposed method is not affected by the observation height. Finally, the proposed forward method is applied to the topography correction of the Moon. The results show that the gravity response of the topography obtained with our method is close to that of the optimized 3D GLQ method and is also consistent with previous results. [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]

We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes. The general solutions are presented for a positive and negative cosmological constant as the only source of the gravity. Matching conditions on a planar boundary between two regions with distinct plane symmetric metric tensors are discussed. An example is considered with Rindler and Taub geometries in neighboring half-spaces. As another example, we discuss a finite thickness cosmological constant slab embedded into the Minkowski, Rindler and Taub spacetimes. The corresponding surface energy-momentum tensor is found required for matching the exterior and interior geometries. [ABSTRACT FROM AUTHOR]

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*. [ABSTRACT FROM AUTHOR]

We have theoretically and experimentally demonstrated the feasibility of achieving ultra-low dark current in CpBnn type detectors based on a double-barrier InAs/GaSb/AlSb type-II superlattice. By employing a structure that separates the absorption region and depletion region, the diffusion, recombination, tunneling, and surface dark currents of the photodetector (PD) have been suppressed. Experimental validation has shown that a detector with a diameter of 500 µm at a bias voltage of −0.5 V exhibits a dark current density of 2.5 × 10−6 A/cm2 at the operating temperature of 300 K. The development of PD with low dark current has paved the way for applications with high demands for low noise in the fields of gravitational wave detection and astronomical observation. [ABSTRACT FROM AUTHOR]

Within the framework of symmetric teleparallel f Q -gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler–DeWitt equation of quantum cosmology. The gravitational field equation in f Q -gravity permits a minisuperspace description, rendering the Wheeler–DeWitt equation a single inhomogeneous partial differential equation. We use the power-law f Q = f 0 Q μ model, and with the application of linear quantum observables, we calculate the wave function of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit. [ABSTRACT FROM AUTHOR]

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field. [ABSTRACT FROM AUTHOR]

To the first post–Newtonian order, the gravitational action of mass–energy currents is encoded by the off–diagonal gravitomagnetic components of the spacetime metric tensor. If they are time–dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source of the gravitational field be an isolated, massive body rigidly rotating whose spin angular momentum experiences a slow precessional motion. The impact of the aforementioned acceleration on the orbital motion of a test particle is analytically worked out in full generality. The resulting averaged rates of change are valid for any orbital configuration of the satellite; furthermore, they hold for an arbitrary orientation of the precessional velocity vector of the spin of the central object. In general, all the orbital elements, with the exception of the mean anomaly at epoch, undergo nonvanishing long–term variations which, in the case of the Juno spacecraft currently orbiting Jupiter and the double pulsar PSR J0737–3039 A/B turn out to be quite small. Such effects might become much more relevant in a star–supermassive black hole scenario; as an example, the relative change of the semimajor axis of a putative test particle orbiting a Kerr black hole as massive as the one at the Galactic Centre at, say, 100 Schwarzschild radii may amount up to about 7 % per year if the hole's spin precessional frequency is 10 % of the particle's orbital one. [ABSTRACT FROM AUTHOR]

We analyze a rotating black hole (BH) in a four-dimensional space-time embedded in five-dimensional flat bulk. In Boyer–Lindquist coordinates, we use a generic extension of the Kerr metric by the line element of Gürses–Gürsey metric. We discuss their horizon properties and shadow cast which is tailored by the influence of the extrinsic curvature. By means of the model based on the Nash–Greene theorem, we analyze the Gürses–Gürsey metric embedded in five dimensions acting as a rotating "charged" BH which may be regarded as a source of ultrahigh-energy cosmic rays (UHECRs). We also show that this type of BH presents a different structure of the accretion disk which is modified by the extrinsic curvature leading to an enlargement of the photons ring and an increase in the BH's inner shadow. In the presence of a magnetic field, our initial results suggest that such BHs may be efficient free-test particle accelerators orbiting the inner stable circular orbit (ISCO). [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]

We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A |$^{\ast \, }$|⁠. After introducing our PPN model of black hole spacetime, we report the result of |$\chi ^2$| fitting of the PPN model with the observational data. A new finding through our PPN model is the detectability of the gravitational lens effect on the null geodesics connecting S0-2 and the observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for the general relativity case. On the other hand, the effect of black hole spin on S0-2's motion is not detectable. Thus, our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum |$\chi ^2$|⁠ , implies that the gravitational field of Sgr A |$^{\ast \, }$| is not of the Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A |$^{\ast \, }$| to be detected by present telescopes. However, the difference between the minimum |$\chi ^2$| and the |$\chi ^2$| of the Schwarzschild case is not large enough to ensure the statistical significance of the non-Schwarzschild result. A more precise statistical analysis than |$\chi ^2$| statistics is necessary to extract statistically significant information on the gravitational field of Sgr A |$^{\ast \, }$| from the present observational data. We will report a result by a Bayesian analysis in our next paper. [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]

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]

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]

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]

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]

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]

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]

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]

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]

We investigate a spherically symmetric exact solution of Einstein's gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions. [ABSTRACT FROM AUTHOR]

In the so-called West, feminist activists and scholars have long been traumatised by the erasure of their histories via dominant patriarchal narratives, which has served as an impediment to the intergenerational transmission of feminist knowledge. Recently, while acknowledging the very real and ongoing impact of this historical omission, some feminists have issued a call to turn away from a narrative of women's history as 'serial forgetting' and towards an acknowledgement of the affirmative capacity of feminist remembering. At the same time, memory theorist Ann Rigney has advocated for a 'positive turn' in memory studies, away from what she perceives to be the field's gravitation towards trauma and instead towards an analysis of life's positive legacies. In this article, I combine both approaches to investigate one feminist memory-keeper's archive, analysing what it reveals about 'the mechanisms by which positive attachments are transmitted across space and time'. Throughout her life, little-known 'between-the-waves' Australian feminist Ruby Rich (1888–1988) performed multiple intersecting activist activities. While she created feminist memories through her work for various political organisations, she also collected, stored and transmitted feminist memories through her campaign for a dedicated space for women's collections in the National Library of Australia. Propelled by fear of loss and inspired by hope for remembering, Rich constructed a brand of archival activism that was both educational and emotional. In this paper, I examine the strategies Rich employed to try to realise her dream of effecting intellectual and affective bonds between future feminists and their predecessors. [ABSTRACT FROM AUTHOR]

In general relativity, the gravitational field of an electrically charged, non-rotating, spherically symmetric body is described by the Reissner–Nordström (RN) metric. Depending on the charge to mass ratio, the solution describes a black hole or a naked singularity. In the naked-singularity regime, a general property of this metric is the existence of a radius, known as the zero-gravity radius, where a test particle would remain at rest. As a consequence of repulsive gravity there is no circular orbit inside this radius, and at least a part of any quasi-stable structure must necessarily lie outside of it. Assuming the iconic torus in the compact source Sgr A* at the Galactic centre observed by the Event Horizon Telescope (EHT) to be the image of a quasi-stationary fluid structure, we provide rigorous constraints in the RN metric on the electric charge-to-mass ratio Q / M of Sgr A*. A comparison between the EHT observations and the space–time zero-gravity radius provides the most conservative limit on the charge of Sgr A* to be | Q / M | < 2.32 in geometrized units. A charged naked singularity respecting this charge-to-mass constraint is consistent with the current EHT observations, if the image is not interpreted as a photon ring. [ABSTRACT FROM AUTHOR]

Using MeerKAT , we have discovered three new millisecond pulsars (MSPs) in the bulge globular cluster M62: M62H, M62I, and M62J. All three are in binary systems, which means all ten known pulsars in the cluster are in binaries. M62H has a planetary-mass companion with a median mass M c, med ∼ 3 MJ and a mean density of ρ ∼ 11 g cm−3. M62I has an orbital period of 0.51 d and a M c, med ∼ 0.15 M⊙. Neither of these low-mass systems exhibit eclipses. M62J has only been detected in the two Ultra High Frequency band (816 MHz) observations with a flux density S 816 = 0.08 mJy. The non-detection in the L-band (1284 MHz) indicates it has a relatively steep spectrum (β < −3.1). We also present 23-yr-long timing solutions obtained using data from the Parkes 'Murriyang', Effelsberg , and MeerKAT telescopes for the six previously known pulsars. For all these pulsars, we measured the second spin-period derivatives and the rate of change of orbital period caused by the gravitational field of the cluster, and their proper motions. From these measurements, we conclude that the pulsars' maximum accelerations are consistent with the maximum cluster acceleration assuming a core-collapsed mass distribution. Studies of the eclipses of the redback M62B and the black widow M62E at four and two different frequency bands, respectively, reveal a frequency dependence with longer and asymmetric eclipses at lower frequencies. The presence of only binary MSPs in this cluster challenges models which suggest that the MSP population of core-collapsed clusters should be dominated by isolated MSPs. [ABSTRACT FROM AUTHOR]

Plants can autonomously adjust their growth direction based on the gravitropic response to maximize energy acquisition, despite lacking nerves and muscles. Endowing soft robots with gravitropism may facilitate the development of self‐regulating systems free of electronics, but remains elusive. Herein, acceleration‐regulated soft actuators are described that can respond to the gravitational field by leveraging the unique fluidity of liquid metal in its self‐limiting oxide skin. The soft actuator is obtained by magnetic printing of the fluidic liquid metal heater circuit on a thermoresponsive liquid crystal elastomer. The Joule heat of the liquid metal circuit with gravity‐regulated resistance can be programmed by changing the actuator's pose to induce the flow of liquid metal. The actuator can autonomously adjust its bending degree by the dynamic interaction between its thermomechanical response and gravity. A gravity‐interactive soft gripper is also created with controllable grasping and releasing by rotating the actuator. Moreover, it is demonstrated that self‐regulated oscillation motion can be achieved by interfacing the actuator with a monostable tape spring, allowing the electronics‐free control of a bionic walker. This work paves the avenue for the development of liquid metal‐based reconfigurable electronics and electronics‐free soft robots that can perceive gravity or acceleration. [ABSTRACT FROM AUTHOR]

This paper investigates the fundamental sensing mechanism of electrostatic MEMS gas sensors. It compares among the responsivities of a set of MEMS isopropanol sensors before and after functionalization, and in the presence and absence of electrostatic fields when operated in static and dynamic detection modes. In the static mode, we found that the sensors do not exhibit a measurable change in displacement due to added mass. On the other hand, bare sensors showed a clear change in displacement in response to isopropanol vapor. In the dynamic mode, functionalized sensors showed a measurable frequency shift due to the added mass of isopropanol vapor. In the presence of strong electrostatic fields, the measured frequency shift was found to be threefold larger than that in their absence in response to the same concentration of isopropanol vapor. The enhanced responsivity of dynamic detection allows the sensors to measure the vapor mass captured by the functional material, which is not the case for static detection. The detection of isopropanol by bare sensors in static mode shows that change in the medium permittivity is the primary sensing mechanism. The enhanced responsivity of dynamic mode sensors when operated in strong electrostatic fields shows that their sensing mechanism is a combination of a weaker added mass effect and a stronger permittivity effect. These findings show that electrostatic MEMS gas sensors are independent of the direction of the gravitational field and are, thus, robust to changes in alignment. It is erroneous to refer to them as 'gravimetric' sensors. [ABSTRACT FROM AUTHOR]

It is already known that a simple nonlocal de Sitter gravity model, which we denote as d S gravity, contains an exact vacuum cosmological solution that mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of d S gravity motivated us to investigate how it works at a lower-than-cosmic scale—galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild–de Sitter metric of the d S gravity model. To obtain an exact solution, it is necessary to solve the corresponding nonlinear differential equation, which is a very complicated and difficult problem. What we obtained is a solution to a linearized equation, which is related to space metrics far from the massive body, where the gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of nonlocal de Sitter gravity d S in describing the effects in galactic dynamics that are usually attributed to dark matter. This solution was tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements. [ABSTRACT FROM AUTHOR]

We show global existence of a measure-valued solution to the Cauchy problem for the rectilinear Euler-Poisson equations, which govern flow of pressureless dust experiencing linear damping in the gravitational field generated by its own mass, and a given background charge field modeling exterior gravitational force. The velocity of the dust is a Borel measurable function, and the distribution of mass is given by time-dependent probability measures on the real line. Upon adapting the method established in Hynd (2020) [25] , we obtain the solution by construction of a probability measure on the path space, through approximation of finite sticky particles. [ABSTRACT FROM AUTHOR]

The gravity and gradient anomalies contain valuable information about the underground geological structures at various depths. Deep and shallow buried source bodies are able to be identified through multi-scale field separation processes, and visual comprehensions of geological structures can be obtained via 3D density inversion techniques. In this study, we propose an improved 3D imaging strategy based on gravitational field separation using the preferential continuation filter. This strategy incorporates the relationship between spectral features and buried depths of source bodies, allowing for a one-step transformation from planar gravity and full-tensor gradient field observations to a 3D density structure in the wave-number domain. Synthetic tests validate the effectiveness and robustness of the gravity and gradient imaging approaches, highlighting their advantages in high vertical resolution and low computational requirements. Nonetheless, it should be noted that the imaging effects of horizontal gradients Γ x x and Γ y y are unsatisfactory due to their weak noise resistance. Thus, they are not suitable for real data applications. The other imaging approaches are further applied to recover the subsurface 3D density structure beneath the Weishan cone in Wudalianchi Volcanic Field, Northeastern China. Our results provide insights into the possible location and shape of the low-density magma chamber. Also, the potential presence of partial melts is inferred and supported from a gravity perspective. The primary advantage of these approaches is their ability to generate a reasonable geological model in scenarios with limited prior information and physical property constraints. As a result, they have significant practical value in the field of applied geophysics, including mineral exploration and volcanology studies. [ABSTRACT FROM AUTHOR]

In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier-Stokes equations. The upper boundary of the fluid is free and evolves within the container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between 0 and π depending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate. [ABSTRACT FROM AUTHOR]

Inspired by the generalization of scalar field gravitational models with a minimum length we study the equivalent theory in modified theories of gravity. The quadratic generalized uncertainty principle (GUP) gives rise to a deformed Heisenberg algebra in the application, resulting in the emergence of additional degrees of freedom described by higher-order derivatives. The new degrees of freedom can be attributed to the introduction of a new scalar field, transforming the resulting theory into a two-scalar field theory. Thus, in order to describe all the degrees of freedom we investigate special forms of the sixth-order modify f R , □ R - theory of gravity, where the gravitational Lagrangian has similar properties to that of the GUP scalar field theory. Finally, the cosmological applications are discussed, and we show that the de Sitter universe can be recovered without introducing a cosmological constant. [ABSTRACT FROM AUTHOR]

We investigate the gravitational field of a charged, non-vacuum, non-rotating, spherically symmetric body of mass M assuming a static solution to the Einstein–Maxwell field equations. We show the characteristics of perihelion precession of orbits in the case of charged naked singularity (CNS) spacetime. Here we discuss some novel features of light-like geodesics in this spacetime. We also discuss the comparative study of tidal force in the null singularity spacetime and charged naked singularity spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a 4D-AdS-Einstein–Gauss–Bonnet black hole. This solution, which finds its inspiration in noncommutative geometry, had previously been established in our previous work. The radius of the shadow was determined using the Hamilton-Jacobi method and the Carter separation. Our results revealed that the presence of noncommutativity in the background of spacetime impacts the variation of the shadow radius. More specifically, we have demonstrated that an increase in the parameter θ induces a decrease in the radius of the shadow. In a similar way, analogous observations have been made by studying the variation of the electric charge Q. The noncommutative parameter θ and the electric charge Q have been constrained regarding the EHT observation data of the M87* and Sgr A* black holes. Furthermore, the angle of deflection, which is the outcome of lensing by the black hole, has been derived following the Ishihara et al. approach for a receiver and source positioned at finite distances from the black hole in an asymptotically non-flat spacetime. The impact of the noncommutative parameter θ and the charge Q of the black hole are hence analyzed, and our results depict that these parameters have a significant influence on the angle at which light is deflected by the gravitational field of the black hole. [ABSTRACT FROM AUTHOR]

Neural architecture search (NAS) is an extremely complex optimization task. Recently, population-based optimization algorithms, such as evolutionary algorithm, have been adopted as search strategies for designing neural networks automatically. Various population-based NAS methods are promising in searching for high-performance neural architectures. The explosion gravitation field algorithm (EGFA) inspired by the formation process of planets is a novel population-based optimization algorithm with excellent global optimization capability and remarkable efficiency, compared with the classical population-based algorithms, such as GA and PSO. Thus, this paper attempts to develop a more efficient NAS method, called EGFA-NAS, by utilizing the work mechanisms of EGFA, which relaxes the search discrete space to a continuous one and then utilizes EGFA and gradient descent to optimize the weights of the candidate architectures in conjunction. To reduce the computational cost, a training strategy by utilizing the population mechanism of EGFA-NAS is proposed. In addition, a weight inheritance strategy for the new generated dust individuals is proposed during the explosion operation to improve performance and efficiency. The performance of EGFA-NAS is investigated in two typical micro search spaces: NAS-Bench-201 and DARTS, and compared with various kinds of state-of-the-art NAS competitors. The experimental results demonstrate that EGFA-NAS is able to match or outperform the state-of-the-art NAS methods on image classification tasks with remarkable efficiency improvement. [ABSTRACT FROM AUTHOR]

Periodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids. While various bifurcations of periodic orbit families around asteroids have been extensively studied, period-multiplying bifurcations have received less attention. This paper focuses on studying period-multiplying bifurcations of periodic orbit families around asteroids. In particular, orbits with periods of approximately 7 and 17 times that of the rotational period of asteroid 216 Kleopatra were computed. The computation of high-period orbits provides insights into the numerical aspects of simulating long-duration trajectories around asteroids. The previous literature uses single-shooting and multiple-shooting methods to compute bifurcations of periodic orbit families around asteroids. Computational difficulties were encountered while using the shooting methods to obtain period-multiplying bifurcations of periodic orbit families around asteroids. This work used the Legendre–Gauss collocation method to compute period-multiplying bifurcations around asteroids. This study recommends the use of collocation methods to obtain long-duration orbits around asteroids when computational difficulties are encountered while using shooting methods. [ABSTRACT FROM AUTHOR]

This paper focuses on the obstacle avoidance trajectory planning problem for autonomous vehicles on structured roads. The objective is to design a trajectory planning algorithm that can ensure vehicle safety and comfort and satisfy the rationality of traffic regulations. This paper proposes a path and speed decoupled planning method for non-split vehicle trajectory planning on structured roads. Firstly, the path planning layer adopts the improved artificial potential field method. The obstacle-repulsive potential field, gravitational potential field, and fitting method of the traditional artificial potential field are improved. Secondly, the speed planning aspect is performed in the Frenet coordinate system. Speed planning is accomplished based on S-T graph construction and solving convex optimization problems. Finally, simulation and experimental verification are performed. The results show that the method proposed in this paper can significantly improve the safety and comfortable riding of the vehicle. [ABSTRACT FROM AUTHOR]

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications. [ABSTRACT FROM AUTHOR]

In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth's crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth's crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model's geometry or gravity data grid. As a case study, a spherical density model of the Earth's crust of the Urals is created. [ABSTRACT FROM AUTHOR]

Based on experimental results and self-consistent physical theory, a three-component description of nonlinear body waves in porous media is constructed. Applications of this result to two-component fluid flow in dynamic porous media and seismic wave propagation in multiphase porous media are presented. This description is important to petroleum reservoir simulation, groundwater hydrology, and seismic analysis of the earth. The two-body analogue of these results has been shown, in the past, to be inconsistent with the two-body linear models currently used by petroleum engineers and groundwater hydrologists. In seismic theory, simple linear models are generally used and much of the information obtained from the theory presented here is referred to as noise. The processes observed and described here have been patented and applied commercially to oil production and groundwater remediation. It is shown here that even if the correct nonlinear equations are used, three-component wave descriptions of porous media cannot be constructed solely from the equations of motion for the components. This is because of the introduction of the complexity of multiple scales into this nonlinear field theory. Information about the coupling between the components is required to obtain a physical description. It is observed that the fields must be coupled in phase and out of phase, and this result is consistent with the description of three- and n-body gravitational fields in Newtonian gravity and general relativity. [ABSTRACT FROM AUTHOR]

We describe an approach to incorporating the physical effects of the absorption of energy by the event horizon of black holes in the scattering amplitudes based post-Minkowskian, point-particle effective description. Absorptive dynamics are incorporated in a model-independent way by coupling the usual point-particle description to an invisible sector of gapless internal degrees-of-freedom. The leading order dynamics of this sector are encoded in the low-energy expansion of a spectral density function obtained by matching an absorption cross section in the ultraviolet description. This information is then recycled using the scattering amplitudes based Kosower-Maybee-O'Connell in-in formalism to calculate the leading absorptive contribution to the impulse and change in rest mass of a Schwarzschild black hole scattering with a second compact body sourcing a massless scalar, electromagnetic or gravitational field. The results obtained are in complete agreement with previous worldline Schwinger-Keldysh calculations and provide an alternative on-shell scattering amplitudes approach to incorporating horizon absorption effects in the gravitational two-body problem. [ABSTRACT FROM AUTHOR]