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This work re-derives and discusses non-Lorentz invariant variable speed of light (VSL) theories in the context of cosmological problems. Following a thorough introduction to the subject, an explicit solution demonstrating a possible dependence of the speed of light on the cosmological scale factor is presented and analyzed. The parameters of the initial ansatz, c (t) = c 0 a n , are constrained by requiring the VSL formulation to be a solution to the flatness and horizon problems. The theoretical section is concluded with a derivation of the change of entropy in a VSL Universe. Even though such findings imply that the speed of light can vary only in non-flat spacetime, an adapted approach using the Generalized Second Law of Thermodynamics is shown to loosen this restriction. Further, in the experimental section, recent evidence for a temporally varying fine structure constant at ≈ 4 σ significance is presented as a potential test for the VSL hypothesis. Overall, this work introduces and evaluates many aspects of non-Lorentz invariant VSL theories whilst encouraging future research and serving as a largely self-sufficient comprehensive overview paper. [ABSTRACT FROM AUTHOR]

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

We have discussed the Dirac equation in Schwarzschild spacetime using pseudo-supersymmetric quantum mechanics and have obtained the partner Hamiltonian of the initial Hamiltonian operator. We demonstrate that the partner metric tensors, corresponding to these Hamiltonians, can be derived using the intertwining relations inherent in pseudo-supersymmetric approaches. We have seen that the Schwarzschild metric may be expanded into Schwarzschild–Tangherlini metric using the aspects of pseudo-supersymmetry. Furthermore, we have derived approximate solutions for the radial component within the framework of N = 2 supersymmetry with the corresponding radial potential graphs presented. Subsequently, our discussion extends to the quasinormal modes, focusing particularly on the asymptotic limits as r approaches ± ∞ . [ABSTRACT FROM AUTHOR]

In this work, we mainly focus on testing the spacetime properties around black holes surrounded by a dark fluid, which are potential candidates for dark energy described by the Chaplygin-like equation of state through its shadow. To do this, we first study the black hole's horizon structure and shadow for the non-rotating case. Then, we obtain a rotating black hole solution in the presence of a dark fluid using the generalized Newman–Janis algorithm and study the effects of the black hole spin and the fluid parameters on the black hole horizons. Also, we obtained the shadow cast of the rotating black hole using celestial coordinates and showed that the presence of the dark fluid causes an increase in shadow size. Moreover, we use the shadow size of supermassive black holes Sagittarius A* and M87* from Event Horizon Telescope observations to obtain constraints on the spin, black hole charge, and dark fluid parameters. Lastly, we investigate the energy emission rate of a charged black hole surrounded by a Chaplygin-like dark fluid, comparing it to both rotating and non-rotating cases. [ABSTRACT FROM AUTHOR]

Conformal Carter–Penrose diagrams are used for the visualization of hyperboloidal slices, which are smooth spacelike slices reaching null infinity. The focus is on the Schwarzschild black hole geometry in spherical symmetry, whose Penrose diagrams are introduced in a pedagogical way. The stationary regime involves time-independent slices. In this case, different options are given for integrating the height function—the main ingredient for constructing hyperboloidal foliations. The dynamical regime considers slices changing in time, which are evolved together with the spacetime using the eikonal equation. It includes the relaxation of hyperboloidal Schwarzschild trumpet slices and the collapse of a massless scalar field into a black hole, for which Penrose diagrams are presented. [ABSTRACT FROM AUTHOR]

We propose an ansatz for encoding the physics of nonlocal spacetime defects in the Green's functions for a scalar field theory defined on a causal set. This allows us to numerically study the effects of nonlocal spacetime defects on the discrete Feynman propagator of the theory defined on the causal set in 1+1 dimensions, and to compare to the defect-free limit. The latter approaches the expected continuum result, on average, when the number of points becomes large. When defects are present, two points with the same invariant spacetime interval can have different propagation amplitudes, depending on whether the propagation is between two ordinary spacetime points, two defects, or a defect and an ordinary point. We show that a coarse-grained description that is only sensitive to the average effect of the defects can be interpreted as a defect-induced mass and wave-function renormalization of the scalar theory. [ABSTRACT FROM AUTHOR]

A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance. [ABSTRACT FROM AUTHOR]

The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q , r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q , r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrödinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the production process of a photon pair in a regime of quantum electrodynamics, considering the presence of a constant four-vector that defines a privileged direction in spacetime, resulting in Lorentz symmetry violation. We explore Lorentz violation in the context of vectorial nonminimal coupling, where we analyze the modifications introduced by this coupling in the scattering amplitude at the vertex. Moreover, we delve into Lorentz violation with axial-like nonminimal coupling. Both analyses are conducted by examining the constant four-vector of both time-like and space-like types. [ABSTRACT FROM AUTHOR]

A popular physical picture of the mechanism behind the four-dimensional chiral anomaly is provided by the massless Dirac equation in the presence of constant electric and magnetic background fields. The magnetic field creates highly degenerate Landau levels, the lowest of which is gapless. Any parallel component of the electric field drives a spectral flow in the gapless mode that causes particles to emerge from, or disappear into, the Dirac sea. Seeking a similar picture for the gravitational contribution to the chiral anomaly, we consider the massless Dirac equation in a background spacetime that creates gravitational Landau levels. We find that in this case the resulting spectral flow, with its explicit particle production, accounts for only a small part of the anomalous creation of chiral charge. The balance is provided by the vacuum expectation charge arising from the spectral asymmetry. [ABSTRACT FROM AUTHOR]

We discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account the internal region of the black hole, the canonical commutation relations in the resulting theory hold exactly and the Hamiltonian has the standard form. Spin sums are obtained for solutions of the Dirac equation in the Schwarzschild spacetime. [ABSTRACT FROM AUTHOR]

We propose a nonlinear quantum walk model inspired in a photonic implementation in which the polarization state of the light field plays the role of the coin-qubit. In particular, we take profit of the nonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows to implement a nonlinear coin operator, one that depends on the state of the coin-qubit. We consider the space-time continuum limit of the evolution equation, which takes the form of a nonlinear Dirac equation. The analysis of this continuum limit allows us to gain some insight into the existence of different solitonic structures, such as bright and dark solitons. We illustrate several properties of these solitons with numerical calculations, including the effect on them of an additional phase simulating an external electric field. [ABSTRACT FROM AUTHOR]

Károlyházy's original proposal, suggesting that space-time fluctuations could be a source of decoherence in space, faced a significant challenge due to an unexpectedly high emission of radiation (13 orders of magnitude more than what was observed in the latest experiment). To address this issue, we reevaluated Károlyházy's assumption that the stochastic metric fluctuation must adhere to a wave equation. By considering more general correlation functions of space-time fluctuations, we resolve the problem and consequently revive the aforementioned proposal. [ABSTRACT FROM AUTHOR]

We investigate asymptotic symmetries which preserve the Bondi gauge conditions but do not preserve the asymptotic falloff conditions for the metric near the null boundary, and their connection to soft graviton theorems for scattering amplitudes. These include generalized superrotation symmetries parameterized by a smooth vector field Y A obeying D A Y A = 0 , for which we show that the associated conserved charge can be derived by applying the Noether procedure to the Einstein–Katz action. We also discuss the connection between asymptotic symmetries and the conserved charge associated with the sub-subleading soft theorem, and we find that in Bondi gauge this charge is generated by the combination of a diffeomorphism together with an extra transformation of the metric. [ABSTRACT FROM AUTHOR]

In this paper, we find the higher-order expansion parameters α and λ of spherically symmetric parameterized Rezzolla–Zhidenko (PRZ) spacetime by using its functions of the radial coordinate. We subject the parameters of this spacetime to classical tests, including weak gravitational field effects in the solar system, observations of the S2 star that is located in the star cluster close to the Sgr A⋆, and of the frequencies of selected microquasars. Based on this spherically symmetric spacetime, we perform the analytic calculations for solar system effects such as perihelion shift, light deflection, and gravitational time delay to determine limits on the parameters by using observational data. We restrict our attention to the limits on the two higher-order expansion parameters α and λ that survive at the horizon or near the horizon of spherically symmetric metrics. The properties of the expansion of these two small parameters in PRZ parameterization are discussed. We further apply Markov Chain Monte Carlo simulations to analyze and obtain the limits on the expansion parameters by using observations of the phenomena of the S2 star. Finally, we consider the epicyclic motions and derive analytic expressions of the epicyclic frequencies. Applying these expressions to the quasiperiodic oscillations of selected microquasars allows us to set further limits on the parameters of the PRZ spacetime. Our results demonstrate that the higher-order expansion parameters can be given in the range α, λ = (−0.09, 0.09) and of order ∼10−2 as a consequence of three different tests and observations. [ABSTRACT FROM AUTHOR]

In 2011 Blanchet and Marsat suggested a fully relativistic version of Milgrom's modified Newtonian dynamics in which the dynamical degrees of freedom consist of the spacetime metric and a foliation of spacetime, the khronon field. This theory is simpler than the alternative relativistic formulations. We show that the theory has a consistent nonrelativistic or slow-motion limit. Blanchet and Marsat showed that in the slow motion limit, the theory reproduces stationary solutions of modified Newtonian dynamics. We show that these solutions are stable to khronon perturbations in the low acceleration regime, for the cases of spherical, cylindrical, and planar symmetry. For nonstationary systems in the low acceleration regime, we show that the khronon field generally gives an order unity correction to the modified Newtonian dynamics. In particular, there will be an order unity correction to the MOND version of Kepler's third law, potentially relevant to ongoing efforts to test MOND using GAIA observations of wide binaries. [ABSTRACT FROM AUTHOR]

We present a study of improving the gravitational waveforms of the coalescing spinless binaries in effective-one-body theory based on the post-Minkowskian approximation. The original 'plus' and 'cross' waveform modes of the gravitational wave generated by coalescing spinless black-hole binaries are extracted from the solution of the null tetrad component of the gravitational perturbed Weyl tensor ψ 4 B in the effective spacetime. To enhance the accuracy of the gravitational waveforms, after Damour et al, the waveforms are factored into five components which are the Minkowskian leading factor h ℓ m M , ϵ , the source S ˆ eff ϵ , the tail effect T ℓ m , the phase factor e i δ ℓ m , and the residual term f ℓ m . In the equal mass ratio case, we find that the reconstructed waveform is closer to the five post-Newtonian result than the original waveform, while the ρ ℓ m f resummation method gives the better results. [ABSTRACT FROM AUTHOR]

We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein's equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of the system: the maximum energy principle applies when we include an entropy term from the singularity of the negative-mass solutions, in addition to the Bekenstein–Hawking term for the entropy of solutions with positive interior mass. Then, the thermodynamic analysis leads to four distinct thermodynamic phases. We also show that all types of solutions can be either thermodynamically stable or dynamically stable, but only solutions with zero interior mass can be both. Since most of our results are analytic, thin shell models emerge as a useful theoretical paradigm for exploring gravitational thermodynamics. Our results provide an additional argument in support of the assignment of entropy to the singularity of negative-mass Schwarzschild spacetimes, and, consequently, to Penrose's conjecture about the assignment of entropy to singularities. [ABSTRACT FROM AUTHOR]

In recent years, significant progress has been made in understanding the global evolution of self-gravitating massive matter in the small-perturbative regime near Minkowski spacetime. To investigate the interaction between a Klein–Gordon equation and Einstein's field equations, we developed a new approach called the Euclidean-hyperboloidal foliation method. This method involves constructing a spacetime foliation that is well-suited for deriving precise decay estimates for wave and Klein–Gordon equations in curved spacetime. In this article, we provide an overview of our method and present a complete proof for a wave-Klein–Gordon model that captures some of the key challenges associated with the Einstein-matter system. [ABSTRACT FROM AUTHOR]

It has been long known that in spacetimes with a positive cosmological constant Λ > 0 the area of spatially stable marginally trapped surfaces (MTSs) has a finite upper bound given by 4 π / Λ. In this paper I show that any such spacetime containing spatially stable MTSs with area approaching indefinitely that bound acquire universal properties generically. Specifically, they all possess generalized 'holographic screens' (i.e. marginally trapped tubes) foliated by MTSs of spherical topology, composed of a dynamical horizon portion and a timelike membrane portion that meet at a distinguished round sphere S ˉ with constant Gaussian curvature —and thus of maximal area 4 π / Λ. All future (past) generalized holographic screens (GHSs) containing S ˉ change signature at S ˉ , and all of them continue towards the past (future) with non-decreasing (non-increasing) area of their MTSs. A future (past) singularity arises. For the future case, these 'ultra-massive spacetimes' Senovilla (2023 Port. Math. 80 133–55) may be more powerful than black holes (BHs), as they can overcome the repulsive Λ-force and render the spacetime as a collapsing Universe without event horizon enclosing those GHSs. It is remarkable that these behaviours do not arise if Λ is non-positive. The results have radical implications on BH mergers and on very compact objects accreting mass from their surroundings—if Λ > 0. [ABSTRACT FROM AUTHOR]

We build a self-consistent relativistic scalar theory of gravitation on a flat Minkowski spacetime from a general field Lagrangian. It is shown that, for parameters that satisfy the equivalence principle, this theory predicts the same outcome as general relativity (GR) for every classical solar-system test. This theory also admits gravitational waves that propagate at the speed of light, and the gravitational radiation energy loss in a binary system is shown to be very similar to the GR prediction. We then analyze the strong gravity regime of the theory for a spherically symmetric configuration and find that there is an effective 'singularity' near the Schwarzschild radius. The main goal of this work is to show that, contrary to what is commonly believed, there are relativistic scalar theories of gravitation defined on a Minkowski spacetime that are not ruled out by the classical solar system tests of GR. [ABSTRACT FROM AUTHOR]

We carefully consider the Shapiro time delay due to black holes and shockwaves in de Sitter spacetime and study the implications for causality. We discuss how causality conditions of AdS and flat spacetime can be applied in de Sitter spacetime, using spatial shifts measured on the boundary to define 'fastest null geodesics' and taking into account the 'stretching' of the de Sitter Penrose diagram. We consider the propagation of a massless spin-1 field with a non-minimal coupling in a de Sitter shockwave background as an illustrative example. We also briefly discuss connections to the average null energy condition. [ABSTRACT FROM AUTHOR]

In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in f (R) theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally f (Q) model specific. We further prove that the energy conservation criterion is equivalent to the affine connection's field equation of f (Q) theory, and except the f (Q) = α Q + β model, the non-linear f (Q) models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless Q itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support. [ABSTRACT FROM AUTHOR]

More than 65 years ago, John Wheeler suggested that quantum uncertainties of the metric would be of order one at the Planck scale, leading to large fluctuations in spacetime geometry and topology, which he termed 'spacetime foam.' In this review I discuss various attempts to implement this idea and to test it, both theoretically and, to a lesser extent, observationally. [ABSTRACT FROM AUTHOR]

Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be dynamically excluded if something like our Universe is to emerge from the theory. Here we show that the most common of these 'bad' causal sets, the Kleitman–Rothschild orders, are strongly suppressed in the gravitational path integral, and we provide evidence that a large class of other 'bad' causal sets are similarly suppressed. It thus becomes plausible that continuum behavior could emerge naturally from causal set quantum theory. [ABSTRACT FROM AUTHOR]

We consider nonlinear effective actions for a spin-2 field, whose 'decoupling' limit gives Fierz–Pauli action in D dimensional maximally symmetric spacetime. We find, especially, the effective action for a partially massless field can take a concise geometrical form. The exact solution for time evolution of the background metric in the model using the effective action is also studied. [ABSTRACT FROM AUTHOR]

We consider a solution of a IKKT-type matrix model which can be considered as a 1+1-dimensional space-time with Minkowski signature and a Big Bounce (BB)-like singularity. A suitable i ε regularization of the Lorentzian matrix integral is proposed, which leads to the standard i ε -prescription for the effective field theory. In particular, the Feynman propagator is recovered locally for late times. This demonstrates that a causal structure and time evolution can emerge in the matrix model, even on non-trivial geometries. We also consider the propagation of modes through the BB, and observe an interesting correlation between the post-BB and pre-BB sheets, which reflects the structure of the brane in target space. [ABSTRACT FROM AUTHOR]

In cosmological group field theory (GFT) models for quantum gravity coupled to a massless scalar field the total volume, seen as a function of the scalar field, follows the classical Friedmann dynamics of a flat Friedmann–Lemaître–Robertson–Walker Universe at low energies while resolving the Big Bang singularity at high energies. An open question is how to generalise these results to other homogeneous cosmologies. Here we take the first steps towards studying anisotropic Bianchi models in GFT, based on the introduction of a new anisotropy observable analogous to the β variables in Misner's parametrisation. In a classical Bianchi I spacetime, β behaves as a massless scalar field and can be used as a (gravitational) relational clock. We construct a GFT model for which in an expanding Universe β initially behaves like its classical analogue before 'decaying' showing a previously studied isotropisation. We support numerical results in GFT by analytical approximations in a toy model. One possible outcome of our work is a definition of relational dynamics in GFT that does not require matter. [ABSTRACT FROM AUTHOR]

A model system of equations that serves as a model for the Einstein field equation in generalised harmonic gauge called the good-bad-ugly system is studied in the region close to null and spatial infinity in Minkowski spacetime. This analysis is performed using H. Friedrich's cylinder construction at spatial infinity and defining suitable conformally rescaled fields. The results are translated to the physical set up to investigate the relation between the polyhomogeneous expansions arising from the analysis of linear fields using the i 0-cylinder framework and those obtained through a heuristic method based on Hörmander's asymptotic system. [ABSTRACT FROM AUTHOR]

We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the method via the so-called Kuchař parametrization of the kinematical phase space. We separate the gauge-invariant dynamics of the three-surfaces from the three-surface deformations induced by linear coordinate transformations. The canonical group of the three-surface deformations and the complete space of gauge-fixing conditions are explicit in our approach. We introduce a frame in the space of gauge-fixing conditions and use it to considerably simplify the prescription for gauge-fixing, partial gauge-fixing and spacetime reconstruction. Finally, we illustrate our approach by considering the perturbed Kasner Universe, for which we discuss two kinds of gauges that correspond respectively to the Coulomb-like and the Lorenz-like gauge in electrodynamics. [ABSTRACT FROM AUTHOR]

Theoretical models suggest the existence of a dark matter spike surrounding the supermassive black holes at the core of galaxies. The spike density is thought to obey a power law that starts at a few times the black hole horizon radius and extends to a distance, R sp, of the order of a kiloparsec. We use the Tolmanâ€"Oppenheimerâ€"Volkoff equations to construct the spacetime metric representing a black hole surrounded by such a dark matter spike. We consider the dark matter to be a perfect fluid, but make no other assumption about its nature. The assumed power-law density provides in principle three parameters with which to work: the power-law exponent Îł sp, the external radius R sp, and the spike density ρ DM sp at R sp. These in turn determine the total mass of the spike. We focus on Sagittarius A* and M87 for which some theoretical and observational bounds exist on the spike parameters. Using these bounds in conjunction with the metric obtained from the Tolmanâ€"Oppenheimerâ€"Volkoff equations, we investigate the possibility of detecting the dark matter spikes surrounding these black holes via the gravitational waves emitted at the ringdown phase of black hole perturbations. Our results suggest that if the spike to black hole mass ratio is roughly constant, greater mass black holes require relatively smaller spike densities to yield potentially observable signals. We find that is unlikely for the spike in M87 to be detected via the ringdown waveform with currently available techniques unless its mass is roughly an order of magnitude larger than existing observational estimates. However, given that the signal increases with black hole mass, dark matter spikes might be observable for more massive galactic black holes in the not too distant future. [ABSTRACT FROM AUTHOR]

In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter ω and the matter amount parameter α. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case (âˆ'1/3 < ω < 0) the deflection angles are expressable as quasi-power series of the dimensionless quantities M / b, b / r s,d and α / M 1+3 ω where M, b, r s,d are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of (âˆ'1 < ω < âˆ'1/3), but with the closest radius r 0 replacing b. In the asymptotically flat (or non-flat) case, the increase of α or decrease of ω will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing α or decreasing ω will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing α or ω will both lead to smaller apparent angles. [ABSTRACT FROM AUTHOR]

We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at I + . This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most four-dimensional. We provide several examples. As a simple corollary it is shown that the only spacetime in which the Killing horizon intersects I + (after a conformal completion) is locally the de Sitter Universe. [ABSTRACT FROM AUTHOR]

In model building studies, it is important to check the energy conditions for the corresponding energyâ€"momentum tensor determined by the gravitational field equations in order to single out physically reasonable models. In this process, one often encounters a situation where the energyâ€"momentum tensor has one off-diagonal ‘spaceâ€"time’ component in the frame with an orthonormal basis in a given spacetime. We derive useful criteria of energyâ€"momentum tensors for their Hawkingâ€"Ellis types and the standard energy conditions in such situations. As demonstrations, we apply those criteria to four different systems. [ABSTRACT FROM AUTHOR]

We present a method to compute exact expressions for optical observables for static spherically symmetric spacetimes in the framework of the bilocal geodesic operator formalism. The expressions are obtained by solving the linear geodesic deviation equations for null geodesics, using the spacetime symmetries and the associated conserved quantities. We solve the equations in two different ways: by varying the geodesics with respect to their initial data and by directly integrating the equation for the geodesic deviation. The results are very general and can be applied to a variety of spacetime models and configurations of the emitter and the observer. We illustrate some of the aspects with an example of Schwarzschild spacetime, focusing on the behaviour of the angular diameter distance, the parallax distance, and the distance slip between the observer and the emitter outside the photon sphere. [ABSTRACT FROM AUTHOR]

The curvature scalar invariants of the Riemann tensor are important in general relativity because they allow a manifestly coordinate invariant characterisation of certain geometrical properties of spacetimes such as, among others, curvature singularities, gravitomagnetism. We calculate explicit analytic expressions for the set of Zakharyâ€"McIntosh curvature invariants for accelerating Kerrâ€"Newman black holes in (anti-)de Sitter spacetime as well as for the Kerrâ€"Newmanâ€"(anti-)de Sitter black hole. These black hole metrics belong to the most general type D solution of the Einsteinâ€"Maxwell equations with a cosmological constant. Explicit analytic expressions for the Eulerâ€"Poincare density invariant, which is relevant for the computation of the Eulerâ€"Poincare characteristic χ (M), and the Kretschmann scalar are also provided for both cases. We perform a detailed plotting of the curvature invariants that reveal a rich structure of the spacetime geometry surrounding the singularity of a rotating, electrically charged and accelerating black hole. These graphs also help us in an exact mathematical way to explore the interior of these black holes. Our explicit closed form expressions show that the above gravitational backgrounds possess a non-trivial Hirzebruch signature density. Possible physical applications of this property for the electromagnetic duality anomaly in curved spacetimes that can spoil helicity conservation are briefly discussed. [ABSTRACT FROM AUTHOR]

We revisit the connection between trajectories of accelerated mirrors and spacetime metrics. We present the general (1 + 1)D effective metric that can be obtained with a fibre-optical analogue through the Kerr effect. Then we introduce a new connection between accelerated mirrors and the optical metric. In particular, we connect them for two specific trajectories: the first one is the black mirror that perfectly recreates the Schwarzchild spacetime. The second one is the Schwarzschildâ€"Planck metric that is a regularized version of the Schwarzschild case. The regularization depends on a length scale that has a clear physical interpretation in the fibre-optical analogue system. We study the geometric properties and the Hawking radiation produced in these new analogue metrics. [ABSTRACT FROM AUTHOR]

The data from the event horizon telescope have provided a novel view of the vicinity of the horizon of a black hole (BH), by imaging the region around the light-ring. They have also raised hopes for measuring in the near future, features of the image (or the shadow) related to higher order effects of photons travelling in these regions, such as the appearance of higher order bright rings produced by more than one windings of photons around the light-ring. While the prospect of measuring these fine features of Kerr BHs is very interesting in itself, there are some even more intriguing prospects for observing novel features of possible non-Kerr objects, in the case that the subjects of our images are not the BH solutions of general relativity. In the hope of sufficient resolution being available in the future, we explore in this work the structure and properties of null geodesics around a Hartle–Thorne (HT) spacetime that includes a deformation from the Kerr spacetime characterised by the quadrupole deformation δq. These spacetimes have been found to exhibit a bifurcation of the equatorial light-ring to two off-equatorial light-rings in a range of δq s and spin parameters. In addition to this, there is a range of parameters where both the equatorial and the off-equatorial light-rings are present. This results in the formation of a pocket that can trap photon orbits. We investigate the properties of these trapped orbits and find that chaotic behaviour emerges. Some of these chaotic orbits are additionally found to be 'sticky' and get trapped close to periodic orbits for long times. We also explore how these novel features affect the shadow and find that the off-equatorial light-rings produce distinctive features that deform its circular shape, while the chaotic behaviour associated to the pocket creates features with fractal structure. These results are shown to be quite general, extending to higher order HT spacetimes. [ABSTRACT FROM AUTHOR]

Special Relativity introduces students to Modern Physics, whose importance in the high school is increasing. Nevertheless its teaching and learning is a critical issue. Different solutions have been developed to overcome the encountered difficulties. In this paper we describe the spacetime globe, a mechanical instrument that allows to experience Special Relativity hands-on. We show how it is possible to treat all the main phenomena foreseen by Special Relativity with simple laboratory experiences, using the idea of Minkowski’s spacetime diagrams. The aim is to develop the use of geometrical approach in learning Special Relativity in high schools. [ABSTRACT FROM AUTHOR]

By using simplified 2D gravitational, non-Lorentz invariant actions constructed from the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a radial observer in Schwarzschild spacetime. We then fully characterize the remnant symmetries corresponding to this near-horizon 2D geometry by solving the motion equations adapted to 2D Milne space. This symmetries, which represent special or privileged diads, acquire the form of uniformly accelerated (Rindler) observers whose constant acceleration is proportional to the black hole mass M. [ABSTRACT FROM AUTHOR]

We consider the most general quadratic metric-affine gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all 17 quadratic invariants (both parity even and odd) in torsion and non-metricity as well as their mixings, along with the terms that are linear in the curvature namely the Ricci scalar and the totally antisymmetric Riemann piece. Adding also a matter sector to the latter we first obtain the field equations for the generalized quadratic theory. Then, using a recent theorem, we successfully find the exact form of the affine connection under some quite general non-degeneracy conditions. Having obtained the exact and unique solution of the affine connection we subsequently derive the closed forms of spacetime torsion and non-metricity and also recast the metric field equations into a GR form with modified source terms that are quadratic in the hypermomentum and linear in its derivatives. We also study the vacuum quadratic theory and prove that in this instance, or more generally for vanishing hypermomentum, the connection becomes the Levi-Civita one. Therefore, we also find exactly to what does the quadratic vacuum theory correspond to. Finally, we generalize our result even further and also discuss the physical consequences and applications of our study. [ABSTRACT FROM AUTHOR]

We revisit the old problem of the self-force on a particle moving in a weak-field spacetime in the context of renewed interest in two-body gravitational scattering. We analytically calculate the scalar, electromagnetic, and gravitational self-force on a particle moving on a straight-line trajectory at a large distance from a Newtonian star, and use these results to find the associated correction to its motion. In the gravitational case we must also include the matter-mediated force, which acts at the same perturbative order as the gravitational self-force. We further augment the gravitational results with geodesic calculations at second order in the central body mass to determine the full, explicit solution to the two-body gravitational scattering problem at second post-Minkowskian order (2PM). We calculate the momentum transfer (which reproduces Westpfahl’s old result), the change in mechanical angular momentum (which matches the radiative flux recently computed by Damour), and the change in mechanical mass moment (the time-space components of the angular momentum tensor), which has not previously appeared. Besides the new 2PM results of explicit trajectories and all conserved quantities, this work clarifies the role of gravitational self-force in PM scattering theory and provides a foundation for higher-order calculations. [ABSTRACT FROM AUTHOR]

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate | x |âˆ' θ , x â†' ∞, θ > 1 where x ∈ Z is the interaction range. The dynamics conserve total momentum, total length and total energy. We prove that the systems evolve macroscopically on superballistic space-time scale (y ε âˆ' 1 , t ε âˆ' θ âˆ' 1 2 ) when 1 < θ < 3, (y ε âˆ' 1 , t ε âˆ' 1 âˆ' log ( ε âˆ' 1 ) âˆ' 1 ) when θ = 3, and hyperbolic space-time scale (yÉ› âˆ'1, tÉ› âˆ'1) when θ > 3. Combining our results and the results in (Suda 2021 Ann. Inst. Henri Poincare B 57 2268â€"2314), we show the existence of two different space-time scales on which the systems evolve. In addition, we prove the fluctuations of the normal modes of the superballistic wave equation, which are analogues of the Riemann invariants and capture fluctuations along the characteristics. For the normal modes, the space-time scale is superdiffusive when 2 < θ â©˝ 4 and diffusive when θ > 4. [ABSTRACT FROM AUTHOR]

This is a comprehensive review of new developments in entropic gravity in light of the Relativistic Transactional Interpretation (RTI). A transactional approach to spacetime events can give rise in a natural way to entropic gravity (in the way originally proposed by Eric Verlinde) while also overcoming extant objections to that research program. The theory also naturally gives rise to a Cosmological Constant and to Modified Newtonian Dynamics (MOND) and thus provides a physical explanation for the phenomena historically attributed to ‘dark energy’ and ‘dark matter’.

Whether the cosmological expansion can influence the local dynamics, below the galaxy clusters scale, has been the subject of intense investigations in the past three decades. In this work, we consider McVittie and Kottler spacetimes, embedding a spherical object in a FLRW spacetime. We calculate the influence of the cosmological expansion on the frequency shift of a resonator and estimate its effect on the exchange of light signals between local observers. In passing, we also clarify some of the statements made in the literature. [ABSTRACT FROM AUTHOR]

We study large deviations in interacting quantum liquids with the polytropic equation of state P (ρ) ∼ ρ γ , where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ⩾ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution. [ABSTRACT FROM AUTHOR]

The quantum vacuum has long been known to be characterized by field correlations between spacetime points. We show that such correlationsâ€"vacuum entanglementâ€"in the environment of near-extremal black holes is significantly amplified (up to ten-fold) relative to their slowly rotating counterparts. We demonstrate this effect for rotating Banadosâ€"Teitelboimâ€"Zanelli black holes by measuring the entanglement through the concurrence extracted from the vacuum via two-level quantum systems (Unruhâ€"DeWitt detectors). The effect is manifest at intermediate distances from the horizon, and is most pronounced for near-extremal small mass black holes. The effect is also robust, holding for all boundary conditions of the field and at large spacelike detector separations. Smaller amplification occurs near the horizon, where we find that the entanglement shadowâ€"a region near the black hole from which entanglement cannot be extractedâ€"is diminished in size as the black hole’s angular momentum increases. [ABSTRACT FROM AUTHOR]

Interactive visualization is a valuable tool for introductory or advanced courses in general relativity as well as for public outreach to provide a deeper understanding of the visual implications due to curved spacetime. In particular, the extreme case of a black hole where the curvature becomes so strong that even light cannot escape, benefits from an interactive visualization where students can investigate the distortion effects by moving objects around. However, the most commonly used technique of four-dimensional general-relativistic ray tracing is still too slow for interactive frame rates. Therefore, we propose an efficient and adaptive polygon rendering method that takes light deflection and light travel time into account. An additional advantage of this method is that it provides a natural demonstration of how multiple images occur and how light travel time affects them. Finally, we present our method using three example scenes: a triangle passing behind a black hole, a sphere orbiting a black hole and an accretion disk with different inclination angles. [ABSTRACT FROM AUTHOR]

The authors previously introduced a diffeomorphism-invariant definition of a homogeneous and isotropic sector of loop quantum gravity (LQG), along with a program to embed loop quantum cosmology (LQC) into it. The present paper works out that program in detail for the simpler, but still physically non-trivial, case where the target of the embedding is the homogeneous, but not isotropic, Bianchi I model. The diffeomorphism-invariant conditions imposing homogeneity and isotropy in the full theory reduce to conditions imposing isotropy on an already homogeneous Bianchi I spacetime. The reduced conditions are invariant under the residual diffeomorphisms still allowed after gauge fixing the Bianchi I model. We show that there is a unique embedding of the quantum isotropic model into the homogeneous quantum Bianchi I model that (a) is covariant with respect to the actions of such residual diffeomorphisms, and (b) intertwines both the (signed) volume operator and at least one directional Hubble rate. That embedding also intertwines all other operators of interest in the respective loop quantum cosmological models, including their Hamiltonian constraints. It thus establishes a precise equivalence between dynamics in the isotropic sector of the Bianchi I model and the quantized isotropic model, and not just their kinematics. We also discuss the adjoint relationship between the embedding map defined here and a projection map previously defined by Ashtekar and Wilson-Ewing. Finally, we highlight certain features that simplify this reduced embedding problem, but which may not have direct analogues in the embedding of homogeneous and isotropic LQC into full LQG. [ABSTRACT FROM AUTHOR]

We use zero angular momentum null geodesics in the Kerrâ€"de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal coordinate and write the asymptotic metric in the Bondiâ€"Sachs gauge. [ABSTRACT FROM AUTHOR]