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General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein's GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR's spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed. [ABSTRACT FROM AUTHOR]

Exploring the cosmological variations of fundamental dimensionless constants, such as the fine-structure constant, α , the proton-to-electron mass ratio, μ , and the gravitational constant, G, is essential for testing new phenomena beyond the standard cosmological models. This study focuses on investigating the potential variation of constants by analyzing strong gravitational fields associated with white dwarf stars. Utilizing the observed spectrum of G191-B2B, we present a new constraint on the cosmological variation of μ over extended time scales, Δ μ / μ = (0. 0 8 4 ± 1. 0 4 4) × 1 0 − 8 , incorporating the gravitational redshift z ≈ 5 × 1 0 − 5 . This finding represents a new tool for checking the parameters for Grand Unified Theories (GUTs). [ABSTRACT FROM AUTHOR]

We study numerically a combined gravitational and nonlinear magnetic lensing effect on electromagnetic flux. A magnetar with a dipole magnetic field and background gravitational field is considered to deflect the light rays which passed through its magnetosphere. We assume a square wave front with sides (1 5 0 × 1 5 0) × 1 0 3 m as a grid with the 1 0 3 m dynamic step. At the nodes of this grid, the rays enter perpendicularly into the cubic area, which covers the main magnetic lensing region with a magnetar at the center. On the basis of general relativity (GR) and nonlinear vacuum electrodynamics, the distribution of rays by the deflection angle in the combined field of the magnetar was obtained. On the basis of the analysis of the obtained data, it is possible to assert that the magnetic field distorts the result of gravitational lensing. Therefore, the magnetar is regarded as a gravitational-magnetic lensing object, wherein the magnetic field induces axial distortion within 1 0 − 6 ∘ . These results are expected to be detectable by modern instruments. [ABSTRACT FROM AUTHOR]

We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass m and the Einstein tensor and the other in terms of the orbital angular velocity and the Einstein tensor. These formulae reproduce the well-known ones for the forward shift in the Schwarzschild spacetime. In a general case, the shift deviates from that in the vacuum spacetime due to a particular combination of the components of the Einstein tensor at the radius r of the orbit. The formulae give a backward shift due to the extended-mass effect in Newtonian gravity. In general relativity, in the weak-field and diffuse regime, the active gravitational mass density, ρ A = (ϵ + p r + 2 p t) / c 2 , plays an important role, where ϵ , p r and p t are the energy density, the radial stress and the tangential stress of the matter field, respectively. We show that the shift is backward if ρ A is beyond a critical value ρ c ≃ 2. 8 × 1 0 − 1 5 g/cm3 (m / M ⊙) 2 (r / a.u.) − 4 , while a forward shift greater than that in the vacuum spacetime instead implies ρ A < 0 , i.e. the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on ρ A in the Solar System and the Galactic Centre. [ABSTRACT FROM AUTHOR]

The performance of quantum information protocols can be impacted by the noninertial motion of parties such as in a gravitational field. Previous studies have primarily focused on the degradation of entanglement for global modes, revealing that bipartite entanglement vanishes in the limit of large acceleration, whereas tripartite entanglement does not. In this study, we examine the impact of acceleration on tripartite Gaussian resource states encoded in spatially localized wave packets. Contrarily to prior findings, we observe that genuine tripartite entanglement (GTE) vanishes in the limit of large acceleration for various initial states and observer trajectories. [ABSTRACT FROM AUTHOR]

It is now widely believed that if the gravitational field is (perturbatively) quantum, it would entangle two massive objects (in spatial superpositions) which were otherwise unentangled to begin with. Recently, actual table-top experiments have been proposed to test this idea in what would be the first detection of perturbative quantum gravity. In this essay, we devise a thought experiment to prove that such gravity-induced entanglement depends on the spacetime curvature and can, in principle, act as an alternate signature of the expanding background. This will open up new and complementary directions to search for such entanglement in curved spacetime and reveal fresh perspectives on it. [ABSTRACT FROM AUTHOR]

We investigate the behavior of expansion free collapsing fluids, as studied by L. Herrera, A. Di Prisco and J. Ospino [Symmetry 15 (2023) 754], in the framework of f (R) gravity, which represents a modification of Einstein's general relativity by establishing a function of the Ricci scalar R in the gravitational action. We explore dynamical equations from Bianchi identities that demonstrate the motion and evolution of physical systems under the influence of gravitational fields. We match the inner and outer geometries of spacetime on the hypersurface to develop junction conditions by using the Misner–Sharp formalism. This allows us to identify the connection between mass functions for the inner and outer space as well as the relationship for heat flux q and radial pressure ℙ r . We also investigate analytical solutions of dissipative fluid distribution that fulfill the vanishing expansion condition together with the vanishing complexity factor constraint. For this, we introduce new constraints that permit the integration of the complex system in f (R) gravity. Next, we extract a set of differential equations that explain the dynamical structure of the dissipative spheres both in geodesic and non-geodesic fluids. Furthermore, we explore the physical characteristics of the obtained solutions, such as heat flux, energy density, shear stress, fluid's temperature along with tangential and radial pressure, to assess their viability in describing real astrophysical systems. [ABSTRACT FROM AUTHOR]

In recent years, the modified theory of gravity known as f (Q) gravity has drawn interest as a potential alternative to general relativity. According to this theory, the gravitational force is determined by a function of the so-called "non-metricity" tensor Q , which expresses how far a particle space-time is from the metric geometry. In contrast to general relativity, which describes the gravitational field using the curvature tensor, f (Q) gravity builds a theory of gravity using the non-metricity tensor. For this class of theories, dynamical system analysis of the background and perturbation equations has been carried out in this work to determine how various models behave cosmologically. Here, the critical points are determined for two f (Q) models from the literature: the power law, f (Q) = Q + m Q n , and the logarithmic, f (Q) = α + β log Q models. The stability behavior and corresponding cosmology are displayed for each critical point. For the power law model, we achieve a matter-dominated saddle point with the right matter perturbation growth rate. For the logarithmic model, we get a saddle point dominated by the geometric component of the f (Q) model with perturbations in the decomposition of matter. For both models, we later achieved a stable and accelerating Universe with constant matter perturbations. [ABSTRACT FROM AUTHOR]

The effects of a gravitomagnetic charge on the thermal radiation properties of a thin accretion disk surrounding a non-rotating black hole are studied. The studied system consists of a non-rotating black hole with a non-zero gravitomagnetic charge and a Novikov–Thorne disk that is thin and optically thick. It is found that the gravitomagnetic charge enhances the gravitational field of the central black hole, resulting in an increase in the event horizon and innermost stable circular orbit (ISCO) radii. However, the maximum flux of radiant energy from the accretion disk is reduced and shifted outward from the central object due to the effect of the gravitomagnetic charge. The thermal profile of the accretion disk also exhibits a similar dependence on the radial coordinate and the gravitomagnetic charge of the black hole. The radiative efficiency of the accretion disk decreases from around 6% to approximately 2% with an increase in the value of the gravitomagnetic charge by l ≃ 3 M. The thermal spectra of the accretion disk are also shifted towards lower frequencies, corresponding to the gravitational redshift of electromagnetic radiation coming from the disk, with an increase in the value of the gravitomagnetic charge. One may conclude that the effect of the gravitomagnetic charge is opposite to the effect of black hole spin. [ABSTRACT FROM AUTHOR]

The main findings of the generalized uncertainty principle (GUP), the phenomenological approach, for instance, the emergence of a minimal measurable length uncertainty, are obtained in various versions from theories of quantum gravity, such as string theory, loop quantum gravity, doubly special relativity and black hole physics. GUP counts for impacts of relativistic energies and finite gravitational fields on the fundamental theories of quantum mechanics (QM), the noncommutation and measurement uncertainty. Utilizing GUP in reconciling principles of general relativity (GR) and QM, thereby enables to draw convincing conclusions about quantum gravity. To resolve the shortcuts reported with the nonrelativistic three-dimensional GUP, namely, violation of Lorentz covariance, dependence on frame of reference, and violation of the linear additional law of momenta, we introduce relativistic four-dimensional generalized uncertainty principle (RGUP) to curved spacetime. To unify GR and QM, we apply the Born reciprocity principle (BRP), distance-momentum duality symmetry and RGUP to estimate the fundamental tensor in discretized curved spacetime. To this end, we generalize Riemann geometry. The Finsler geometry, which is characterized by manifold and Finsler structure, allows to directly apply RGUP to the Finsler structure of a free particle so that F ( x ̂ 0 , ẋ 0) can be expressed as F ( x ̂ 0 , ϕ ̂ p ̂ 0) , from which the metric tensor in discretized Riemann spacetime could be deduced. We conclude that F ( x ̂ 0 , ϕ ̂ p ̂ 0) is homogeneous with degree 1 in p ̂ 0 , while ϕ ̂ = 1 + β 1 p ̂ 0 ρ p ̂ 0 ρ is 0 -homogeneous resulting in g ̃ μ ν ≃ (+ 2 β 1 F 2) [ 1 + m ̄ 2 | ẍ ̂ | 2 ] g μ ν . Despite, the astonishing similarity with the conformal transformation, know as Weyl tensor, this study suggests that principles of QMs could be unambiguously imposed on the resulting fundamental tensor. Also, we conclude that the features of Finsler geometry assumed in this study are likely the ones of the duel Hamilton geometry. [ABSTRACT FROM AUTHOR]

For the electromagnetic field in (D + 1) -dimensional locally de Sitter (dS) spacetime, we analyze the effects of a generalized cosmic string type defect on the vacuum expectation value of the energy-momentum tensor. For the Bunch–Davies vacuum state, the topological contributions are explicitly extracted in both the diagonal and off-diagonal components. The latter describes the presence of radially directed energy flux in the vacuum state. It vanishes for D = 3 because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for D ≥ 4. The topological contributions in the vacuum stresses are anisotropic and, unlike the geometry of a cosmic string in the Minkowski spacetime, for D > 3 the stresses along the directions parallel to the string core differ from the energy density. Depending on the planar angle deficit and the distance from the cosmic string, the corresponding expectation values can be either positive or negative. Near the cosmic string the effect of the gravitational field on the diagonal components of the topological part is weak and the leading terms in the respective expansions coincide with the expectation values for a cosmic string in the background of Minkowski spacetime. The spacetime curvature essentially modifies the behavior of the topological terms at proper distances from the cosmic string larger than the dS curvature radius. In that region, the topological contributions in the diagonal components of the energy–momentum tensor decay in inverse proportion to the fourth power of the proper distance and the energy flux density behaves as inverse-fifth power for all values of the spatial dimension D. The exception is the energy density in the special case D = 4. For a cosmic string in the Minkowski bulk the energy flux is absent and the diagonal components are proportional to the (D + 1) th power of the inverse distance. [ABSTRACT FROM AUTHOR]

Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field (X , − X) , which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy–momentum of the gravitational field. It solves the problem of the nonlocalization of gravitational energy–momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully–Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein–Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies. [ABSTRACT FROM AUTHOR]

We study the geodesic deviation equation for a quantum particle in a linearized quantum gravitational field. Particle's Heisenberg equations of motion are treated as stochastic equations with a quantum noise. We explore the stochastic equation beyond its local approximation as a differential equation. We discuss the squeezed states resulting from an inflationary evolution. We calculate the noise in the thermal and squeezed states. [ABSTRACT FROM AUTHOR]

In this paper, we study the evolution of random hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition. The behavior of HMFs is driven by the analog of the chiral magnetic effect accounting for the asymmetries of leptons and Higgs bosons. These asymmetries are also dynamical variables of the model and evolve together with HMFs. Moreover, we account for the contribution of the hyper-MHD turbulence in the effective diffusion coefficient and the α -dynamo parameter. The realistic spectrum of seed HMFs consists of two branches: Batchelor and Kolmogorov ones. The impact of HMFs on the production of relic gravitational waves (GWs) and the baryon asymmetry of the universe (BAU), as well as flavor oscillations of supernova neutrinos in the stochastic GWs generated is considered. We establish the constraint on the strength of the seed HMF comparing the spectral density of produced GWs with the observations of the LIGO-Virgo-KAGRA collaborations. The stronger upper bound on the seed HMF is obtained from the condition of not exceeding the observed value of BAU. [ABSTRACT FROM AUTHOR]

In this work, we explore the wormhole physics in a modified gravitational theory, called the generalized Brans–Dicke theory (GBD). In order to solve the equations in this theory, the parameterized forms for the shape function and the scalar-field function are taken. With the help of selecting a specific form of state equation, i.e. considering a relation between the transverse pressure (not the total pressure) and the energy density for matter that threads wormhole: p t = α ρ = − ρ , we provide some special solutions of the traversable wormhole in GBD. Given that the violation of energy conditions (ECs) of matter often induces problems on the gravitational theory, it is important to inspect the ECs of matter in modified theories. In this GBD theory, we find that the weak energy condition, the null energy condition, the dominated energy condition and the strong energy condition could be satisfied for the matter near the throat of wormhole, depending on the parameterized models and the model-parameters values. Finally, using the classical reconstruction technique in the traversable wormhole physics, we derive a Lagrangian function of gravitational field for the GBD theory. [ABSTRACT FROM AUTHOR]

Massive particles in spatially nonlocal, quantum mechanical wave functions should have interesting gravitational fields. Should their gravitational fields be classical? What aspects of their gravitational fields are observable? We study these questions using quantum field theory to gravitationally probe the wave functions of such quantum mechanical states. We find that the observable signals seem to indicate that it is very difficult to phenomenologically observe the quantum mechanical, spatially nonlocal superposition. [ABSTRACT FROM AUTHOR]

In this paper, we review modified theories of gravity with a curvature–matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a nonvanishing covariant derivative of the energy–momentum tensor, that implies nongeodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard Λ CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form L m R ̃ 2 , where L m is the ordinary matter Lagrangian, and R ̃ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing R ̃ 2 with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant f (R , L m) -type theory, with the matter Lagrangian nonminimally coupled to geometry. [ABSTRACT FROM AUTHOR]

The Randall–Sundrum models are expected to modify the short distance behaviour of general relativity. In this paper, we will propose an experimental test for this short distance modification due to Randall–Sundrum models. This will be done by the analysing motion of a particle which is moving in spherical gravitational field with a drag force. The position at which the particle stops will be different in general relativity and Randall–Sundrum model. This difference in the distance moved by the particle before stopping can be measured using a nanoelectromechanical setup. Thus, it is possible to experimentally test Randall–Sundrum models using currently available technology. [ABSTRACT FROM AUTHOR]

In this paper, we take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schrödinger equation for the particle by starting from the fully relativistic Klein–Gordon equation in order (i) to briefly discuss the issue of the equivalence principle and (ii) to be able to compare the relativistic terms in the equation to the tidal-force terms. To the second order of the nonrelativistic approximation, the resulting Schrödinger equation is that of a simple harmonic oscillator in the horizontal direction and that of an inverted harmonic oscillator in the vertical direction. Two methods are used for solving the equation in the vertical direction. The first method is based on a fixed boundary condition, and yields a discrete-energy spectrum with a wavefunction that is asymptotic to that of a particle in a linear gravitational field. The second method is based on time-varying boundary conditions and yields a quantized-energy spectrum that is decaying in time. Moving on to a freely-falling reference frame, we derive the corresponding time-dependent energy spectrum. The effects of tidal forces yield an expectation value for the Hamiltonian and a relative change in time of a wavepacket's width that are mass-independent. The equivalence principle, which we understand here as the empirical equivalence between gravitation and inertia, is discussed based on these various results. For completeness, we briefly discuss the consequences expected to be obtained for a Bose–Einstein condensate or a superfluid in free fall using the nonlinear Gross–Pitaevskii equation. [ABSTRACT FROM AUTHOR]

We discuss a recent proposal that the Euclidean gravity approach to quantum gravity is correct if and only if the theory is holographic, providing several examples and general arguments to support the conjecture. This provides a natural mechanism for the low-energy gravitational effective field theory to access a host of deep ultraviolet properties, like the Bekenstein–Hawking entropy of black holes, the unitarity of black hole evaporation, and the lack of exact global symmetries. [ABSTRACT FROM AUTHOR]

Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism, a vector potential, the gravitomagnetic potential, arises as a result of moving masses, in strong analogy with the magnetic force due to moving charges in Maxwell's theory. Gravitomagnetism can affect orbits in the gravitational field of a massive, rotating body. This raises the possibility that gravitomagnetism may serve as the dominant physics behind the anomalous rotation curves of spiral galaxies, eliminating the need for dark matter. In this essay, we methodically work out the magnitude of the gravitomagnetic equivalent of the Lorentz force and apply the result to the Milky Way. We find that the resulting contribution is too small to produce an observable effect on these orbits. We also investigate the impact of cosmological boundary conditions on the result and find that these, too, are negligible. [ABSTRACT FROM AUTHOR]

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary. [ABSTRACT FROM AUTHOR]

We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions. [ABSTRACT FROM AUTHOR]

We show the appearance of geometric phase in a Dirac particle traversing in nonrelativistic limit in a time-independent gravitational field. This turns out to be similar to the one originally described as a geometric phase in magnetic fields. We explore the geometric phase in the Kerr and Schwarzschild geometries, which have significant astrophysical implications. Nevertheless, the work can be extended to any spacetime background including that of time-dependent. In the Kerr background, i.e. around a rotating black hole, geometric phase reveals both the Aharonov–Bohm effect and Pancharatnam–Berry phase. However, in a Schwarzschild geometry, i.e. around a nonrotating black hole, only the latter emerges. We expect that our assertions can be validated in both the strong gravity scenarios, like the spacetime around black holes, and weak gravity environment around Earth. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the secular changes of the orbital elements of a planet in the solar system, determined by the magnetic-like part of a gravitational wave field. Using Fermi coordinates, we show that the total force acting on a test particle is made of two contributions: a gravito-electric one and a gravito-magnetic one. While the electric-like force has been thoroughly discussed in the past, the effect of the gravito-magnetic force, which depends on the velocity of the test particle, has not been considered yet. We obtain approximated results to some orders in the orbital eccentricity and show that these effects are much smaller than the corresponding gravito-electric ones. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the entropy of the free gravitational field for a given epoch for some well-known isotropic and anisotropic cosmologies. We use the definition of gravitational entropy proposed by Clifton, Ellis and Tavakol, where the 2-index square root of the 4-index Bel–Robinson tensor is taken to be the energy– momentum tensor for the free gravity. We examine whether in the vicinity of the initial singularity, the ratio of energy density of free gravity to that of matter density goes to zero, validating Penrose conjecture on Weyl curvature. Whenever this is true, the gravitational entropy increases monotonically with time, leading to structure formation. For the models considered by us, we identify the conditions for which the Weyl curvature hypothesis is valid, and the assumptions under which it is validated, or otherwise. [ABSTRACT FROM AUTHOR]

We consider a model of exponential electrodynamics as a source of gravitational field and worked for the solution describing magnetic black hole surrounded by a quintessence and cloud of strings. In this set up, a new family of Lovelock black hole solutions of the gravitational field equations are constructed. The thermodynamics of these black holes is also studied and the mass as well as the other associated thermodynamic quantities such as Hawking temperature and heat capacity in terms of horizon radius are computed. These quantities are dependent on the parameters of exponential electrodynamics, cloud of strings and quintessential dark energy, which have been used for the identification of the regions corresponding to thermal phase transitions and thermodynamic stability of black holes. Furthermore, the effects of thermal fluctuations are also discussed and modified thermodynamic quantities associated to logarithmic correction in entropy are calculated. The Hawking radiations corresponding to these black holes are briefly discussed as well. [ABSTRACT FROM AUTHOR]

The interaction of massless minimally coupled scalar field and spinor field (Ψ + Φ m → Ψ + Φ m) is investigated and the behavior of interaction and scattering matrix in Minkowski limit is studied. It is seen that the massless minimally coupled scalar field operator, the interaction Lagrangian and the scattering matrix become zero. Also, the incoming and outgoing spinor fields, which in de Sitter spacetime are different and are interacted with massless minimally coupled scalar field, in null curvature limit are the same and no interaction seen. In other words, the massless minimally coupled scalar field is dependent on curvature and can be considered as a part of a gravitational field. [ABSTRACT FROM AUTHOR]

Static (not stationary) solutions of the Einstein–Klein–Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated. [ABSTRACT FROM AUTHOR]

Cosmic strings, as remnants of the symmetry breaking phase in the Early universe, may be susceptible to nonlocal physics. Here, we show that the presence of a Poincaré-invariant nonlocality—parametrized by a factor exp (− □ ℓ 2) —regularizes the gravitational field and thereby changes the properties of spacetime: it is now simply connected and the angle deficit around the cosmic string becomes a function of the radial distance. Similar changes occur for the nonlocal gravitomagnetic field of a rotating cosmic string, and we translate these mathematical facts into the language of nonlocal gravitoelectromagnetism and thereby provide a physical interpretation. We hope that these insights might provide a helpful perspective in the search for traces of nonlocal physics in our universe. [ABSTRACT FROM AUTHOR]

Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this paper, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outflows observed at the centers of active galaxies may give evidence for the gravitomagnetic fields of spinning supermassive black holes. We also question whether the current issues in our contemporary observations might be resolved by the inclusion of gravitomagnetism on large scales in a perturbed FLRW model. [ABSTRACT FROM AUTHOR]

We show that when the gravitational field is treated quantum-mechanically, it induces fluctuations — noise — in the lengths of the arms of gravitational wave detectors. The characteristics of the noise depend on the quantum state of the gravitational field and can be calculated exactly in several interesting cases. For coherent states, the noise is very small, but it can be greatly enhanced in thermal and (especially) squeezed states. Detection of this fundamental noise would constitute direct evidence for the quantization of gravity and the existence of gravitons. [ABSTRACT FROM AUTHOR]

The scalar–spinor interaction Lagrangian is presented by the Yukawa potential. In dS ambient space formalism, the interaction Lagrangian of scalar–spinor fields was obtained from a new transformation which is very similar to the gauge theory. The interaction of massless minimally coupled (mmc) scalar and spinor fields was investigated. The Minkowski limit of the mmc scalar field and massive spinor field interaction in the ambient space formalism of de Sitter spacetime is calculated. The interaction Lagrangian and mmc scalar field in the null curvature limit become zero and the local transformation in the null curvature limit become a constant phase transformation and the interaction in this limit become zero. The covariant derivative reduces to ordinary derivative too. Then, we conclude that this interaction is due to the curvature of spacetime and then the mmc scalar field may be a part of a gravitational field. [ABSTRACT FROM AUTHOR]

Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the late-time cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the Hilbert–Einstein action describe the gravitational field, in particular, f (R) gravity, where R is the curvature scalar. In this review, we perform a detailed theoretical and phenomenological analysis of specific modified theories of gravity and investigate their astrophysical and cosmological applications. We present essentially two largely explored extensions of f (R) gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of f (R) gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of f (R) gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a nonvanishing covariant derivative of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory. [ABSTRACT FROM AUTHOR]

We consider the distribution of the axionic dark matter and the profiles of the axionically induced electric field on the background of a regular magnetic monopole. The background static spherically symmetric spacetime is considered to be regular at the center of the object; it has no event horizons, the nonminimal interaction of strong gravitational and monopole type magnetic fields being the source of this regularity. We assume the pseudoscalar (axion) field to be nonminimally coupled to the electromagnetic and gravitational fields, and we search for solutions to the extended equations of nonminimal axion electrostatics, which satisfy two requirements: first, the axionically induced radial electric field vanishes at the center; second, the pseudoscalar field is regular at the center of the formed axionic dyon. We have found the set of parameters, describing the nonminimal axion-photon coupling, for which both requirements are satisfied. Properties of the two-parameter family of regular solutions to the equations of nonminimal axion electrostatics are analyzed numerically. The regular axionically induced electric field is shown to have the structure, which is typical for a simple electric layer. [ABSTRACT FROM AUTHOR]

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope (EHT) observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr–Newman (KN) solution, and the other within the context of low-energy heterotic string theory, the Kerr–Sen (KS) solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions. [ABSTRACT FROM AUTHOR]

I describe the work done in collaboration with A. Belenchia, F. Giacomini, E. Castro-Ruiz, C. Bruckner and M. Aspelmeyer that analyzes a gedanken experiment involving a massive body that is put into a quantum superposition. Remarkably, even for a nonrelativistic body, both vacuum fluctuations of the gravitational field and the quantization of gravitational radiation are essential in order to avoid inconsistencies. In addition, it is essential that the quantum body be viewed as entangled with its own Newtonian-like gravitational field in order to understand how the body may become entangled with other massive bodies via gravitational interactions. [ABSTRACT FROM AUTHOR]

In 1911, Einstein proposed that light bending by the Sun's gravitational field could be measured during a total solar eclipse. The first opportunity in which this measurement would be tried was during the total solar eclipse of October 10, 1912. We report about the expeditions sent to Brazil to observe this eclipse, including the one from the Córdoba Observatory, from Argentina, which aimed to measure this Einstein's effect. [ABSTRACT FROM AUTHOR]

In the weak field approximation, we study the gravitational lensing by spherical symmetric compact object immersed in magnetic field in the presence of magnetized plasma. The external magnetic field causes the split of the deflection angle of the photon, Einstein ring and Einstein cross as the counterpart of the Zeeman effect. In particular, the magnetic field affects the magnification of images, creating additional components. We also study the time delay of an electromagnetic signal due to the geometry and the gravitational field around the lensing source. We show that the time delay of the electromagnetic signal strongly depends on the plasma parameters, and it slightly decreases in the plasma in comparison with that in vacuum. [ABSTRACT FROM AUTHOR]

Recently (Int. J. Mod. Phys. D 27 (2018) 1847025) an interesting property of closed light rings in Kerr black holes has been noticed. We explain its origin and derive a slightly more general result. [ABSTRACT FROM AUTHOR]

When a massive quantum body is put into a spatial superposition, it is of interest to consider the quantum aspects of the gravitational field sourced by the body. We argue that in order to understand how the body may become entangled with other massive bodies via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. Thus, a Newtonian-like gravitational field must be capable of carrying quantum information. Our analysis supports the view that table-top experiments testing entanglement of systems interacting via gravity do probe the quantum nature of gravity, even if no "gravitons" are emitted during the experiment. [ABSTRACT FROM AUTHOR]

Cosmological solution to the gravitational field equations in the generalized Randall–Sundrum model for an anisotropic brane with Bianchi-I geometry and perfect fluid as matter sources has been considered. The matter on the brane is described by a tachyonic field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario: in the first case, universe evolves from singularity and in the second case, universe expands without singularity. [ABSTRACT FROM AUTHOR]

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, m ≠ m e + E 1 c 2 , where the electron is initially in its ground state; m e is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein's famous equation, m ≠ E c 2 . In this paper, we also improve several drawbacks of the original pioneering works. [ABSTRACT FROM AUTHOR]

Einstein, Infeld and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This report identifies necessary conditions for a well-defined general-relativistic joint initial value problem of N classical point charges and their electromagnetic and gravitational fields. Among them, in particular, is the requirement that the electromagnetic vacuum law guarantees a finite field energy–momentum of a point charge. This disqualifies the Maxwell(–Lorentz) law used by EIH. On the positive side, if the electromagnetic vacuum law of Bopp, Landé–Thomas and Podolsky (BLTP) is used, and the singularities equipped with a nonzero bare rest mass, then a joint initial value problem can be formulated in the spirit of the EIH proposal, and shown to be locally well-posed — in the special-relativistic zero- G limit. With gravitational coupling (i.e. G > 0), though, changing Maxwell's into the BLTP law and assigning a bare rest mass to the singularities is by itself not sufficient to obtain even a merely well-defined joint initial value problem: the gravitational coupling also needs to be changed, conceivably in the manner of Jordan and Brans–Dicke. [ABSTRACT FROM AUTHOR]

A modified Brans–Dicke theory (abbreviated as GBD) is proposed by generalizing the Ricci scalar R to an arbitrary function f (R) in the original BD action. It can be found that the GBD theory has some interesting properties, such as solving the problem of PPN value without introducing the so-called chameleon mechanism (comparing with the f (R) modified gravity), making the state parameter to crossover the phantom boundary: w = − 1 without introducing the negative kinetic term (comparing with the quintom model). In the GBD theory, the gravitational field equation and the cosmological evolutional equations have been derived. In the framework of cosmology, we apply the dynamical system approach to investigate the stability of the GBD model. A five-variable cosmological dynamical system and three critical points ( P 1 , P 2 , P 3 ) are obtained in the GBD model. After calculation, it is shown that the critical point P 1 corresponds to the radiation dominated universe and it is unstable. The critical point P 2 is unstable, which corresponds to the geometrical dark energy dominated universe. While for case of P 3 , according to the center manifold theory, this critical point is stable, and it corresponds to geometrical dark energy dominated de Sitter universe ( w tot eff = − 1). [ABSTRACT FROM AUTHOR]

In this paper, we study the model of the late universe with the homogeneous, isotropic and flat Friedmann–Robertson–Walker metric, where the source of the gravitational field is based on the fermion and boson fields, with the Maxwell term F μ ν F μ ν in four dimensions. The actuation of the Maxwell term for the Einstein gravity makes it possible to find new approaches to solve the problem of the observed accelerated expansion of the universe. Energy conditions have been obtained and studied. These conditions impose very simple and model-independent restrictions on the behavior of energy density and pressure since they do not require a specific equation-of-state of matter. To consider the model, the energy conditions NEC, WEC, DEC are realized, and the SEC condition is violated. The boson and fermion fields are responsible for the accelerated regime at early times, but since the total pressure tends toward zero for large times, a transition to a decelerated regime occurs. Maxwell field is crucial only in the early times. [ABSTRACT FROM AUTHOR]

The spin state of a wave packet of a spin-1/2 particle in a gravitational field is a mixed state, obtained by integrating out the momentum degree of freedom. The entropy of this spin mixed state depends on the deviation of spacetime from the flatness. In terms of a succession of local inertial frames, it is shown that spin decoherence occurs even if the particle is uniformly moving or static in a gravitational field. [ABSTRACT FROM AUTHOR]

Gravitational waves (GWs) in Modified Gravity are discussed and compared with General Relativity in view of possible detection of new modes. After a summary of some classes of modified theories, we recall GWs properties in General Relativity as the basic standard by which to compare any modified theory. Then, we discuss GWs in Extended Theories like f (R) gravity, scalar–tensor gravity, Gauss–Bonnet gravity and other gauge theories, as well as Teleparallel Equivalent General Relativity (TEGR), taking into account also torsion instead of curvature, to describe the gravitational field. As a general remark, all these theories lead to new polarizations in addition to the two standard modes of General Relativity. It is possible to show that, in 4 dimensions, the polarizations are at most 6. Theoretical and experimental implications of new modes are briefly discussed. [ABSTRACT FROM AUTHOR]