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In this paper, we review the main features of modified theories of gravity containing higher-order curvature invariants in the action. After summarizing the main features of these theories, we consider their applications to cosmology, pointing out the differences with respect to general relativity that can eventually solve issues exhibited by the latter at low and high energy scales. Specifically, we explore a gravitational action that incorporates both the Ricci scalar R and the topological Gauss–Bonnet term, denoted as . Our investigation revolves around the cosmological properties of a specific category of modified gravity theories, chosen upon symmetry considerations. Within the framework of a spatially flat, homogeneous and isotropic cosmic background, we demonstrate that it is possible to account for the presently observed acceleration of the Universe by means of the extra geometric terms carried by the selected f (R ,) model. This approach offers a way to address the issues associated with the cosmological constant. To achieve this, we first examine the energy conditions and find that, under certain choices for the values of the cosmographic parameters, these conditions are all violated. In the second part of the work, to assess the feasibility of the selected f (R ,) model, we place observational constraints on its free parameters through a Bayesian Monte Carlo technique applied to late-time cosmic data. Our findings reveal that the f (R ,) model can effectively reproduce observations at low redshifts, providing an alternative to the standard Λ CDM scenario. [ABSTRACT FROM AUTHOR]

In this paper, we involve the galactic halo observational data to test the weak field General Relativity involving the cosmological constant. By using the data for 15 hydrogen (Hi) VLA super spirals and the Tully–Fisher relation, we obtain constraints for each galaxy. The results are consistent with previous results for spiral galaxies, as well as with the scaling relations for the halos, thus confirming the efficiency of the use of dark halo data and Tully–Fisher relation, including the baryonic Tully–Fisher index (BTFR), for testing modified gravity models. [ABSTRACT FROM AUTHOR]

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined. [ABSTRACT FROM AUTHOR]

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we have revisited the Berman's idea of the variation of Hubble parameter. While previously explored in the context of Λ-varying cosmologies, where scale factor variations yield linear universe expansion, this parametrization has undergone extensive scrutiny. Our investigation, however, explores into its implications in the context of late-time cosmic acceleration, within the framework of classical general relativity, adopting the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime as our background metric. Our analysis offers a precise solution to Einstein's field equations (EFEs) in a model-independent way, affording a thorough assessment of both geometrical and physical model parameters. Additionally, this study supplements its findings with graphical representations of the evolving cosmological parameters across flat, closed, and open universe scenarios, all subject to constraints derived from the model parameters. In synthesizing these results, we shed light on the intricate interplay between cosmic acceleration, dark energy, and the parametrization of the Hubble parameter, thereby providing valuable insights into the fundamental mechanics of our universe. [ABSTRACT FROM AUTHOR]

This is the fourth paper of our series studying winds from hot accretion flows around black holes. In the first two papers, we showed the existence of strong winds in hot accretion flows using hydrodynamical and magnetohydrodynamical (MHD) simulations. In the third paper, by using three-dimensional general relativity MHD numerical simulation data of hot accretion flows and adopting a "virtual particle trajectory" data analysis approach, we calculated the properties of wind, such as its mass flux and velocity. However, that paper focuses only on a nonspinning black hole and standard and normal accretion. In the present paper, we extend the third paper by including cases of a rapidly rotating black hole and magnetically arrested disk. We focus on investigating the effect of spin and magnetic field on the properties of the wind and jet. It is found that a larger spin and stronger magnetic field usually enhance the wind and jet. The formulae describing the mass flux, poloidal velocity, and fluxes of momentum, kinetic energy, and total energy of the wind and jet are presented. One interesting finding, among others, is that even in the case of a very rapidly spinning black hole, where the jet is supposed to be the strongest, the momentum flux of the jet is smaller than that of the wind, while the total energy flux of the jet is larger than that of the wind by at most a factor of 10. This result suggests that the wind potentially plays a more important role than the jet, at least for some problems in active galactic nucleus feedback. [ABSTRACT FROM AUTHOR]

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This paper introduces the current special issue focussed on the MICROSCOPE mission. This mission is the first experimental test in space of the weak equivalence principle (WEP) using man-made test-massesâ€"as opposed to astronomical testsâ€"with the goal to reach a precision two orders of magnitude better than ground-based experiments. Selected in 1999 by CNES as part of its MYRIADE microsatellite programme, the satellite was launched in 2016 and the mission lasted 2.5 years. This paper summarises the articles of the special issue and highlights the key technological and data analysis aspects that allowed for an unprecedented precision on the test of the WEP. [ABSTRACT FROM AUTHOR]

The gravitational interaction has mass of only one sign as the source that is conventionally taken to be positive. The existence of negative mass is not precluded in either Newtonian gravity or general relativity. Negative masses have been invoked in many recent papers to understand the dominance of repulsive dark energy that is accelerating the universe. Here we discuss the various gravitating properties of negative mass particles and their implications for black holes, cosmology, and fundamental physics. Inconsistencies in the earlier works are also discussed. We study the possibility of such negative mass particles accounting for the accelerated expansion of the universe. We set constraints on the density of these negative mass particles based on astrophysical observations. [ABSTRACT FROM AUTHOR]

In this paper, we have studied conharmonic curvature inheritance (Conh CI) symmetry and its physical importance on the spacetime of general relativity. Also, we have obtained some new results which are direct consequence of proper conformal symmetries. The necessary conditions for a Conh CI vector to be a conformal Killing vector (CKV) have been obtained and results for establishing its relationship between the other known symmetries of spacetimes in general and Einstein spacetimes have been derived. Conh CI with conharmonic motion has been discussed and it is found that a proper Conh CI can produce a new physically relevant solution for perfect fluid spacetime. For Conh CI with conformal Killing vector in perfect fluid spacetime, the equations of state have also been obtained. [ABSTRACT FROM AUTHOR]

Current gravitational waveform models used by detection data analysis have not included the effect of the moving speed of the sources relative to detector. Few works about the gravitational waveform problem for moving sources exist in the literature. And all of them have taken some approximations. Some of them just considered frequency shift. Some of them used slow speed approximation. In the current paper, we apply the precise Lorentz transformation of gravitational wave to generate the gravitational waveform for moving sources with any high speed. Our calculation is straightforward but without any approximation. That is to say our result is valid in the whole velocity range 0 â©˝ v < c which is only limited by the speed of light coming from general relativity itself. If only a waveform model of a rest source is given, our result can be applied directly to generate the waveform for the corresponding moving source with any high speed. Such waveform is valid for binary black hole coalescence happening extremely close to a super-massive black hole. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented in the current paper. [ABSTRACT FROM AUTHOR]

In recent years, a class of compact objects called gravastars have drawn immense interest as regular solutions to end state stellar collapse. Since the energy density involved in collapse process is expected to be high, it is a natural choice to study such compact objects in context of modified gravity theories which reduce to General Relativity (GR) in the low energy regime. We have already framed a model of gravastar in such a modified gravity framework involving extra dimensional Randall–Sundrum (RS) single brane gravity [R. Sengupta, S. Ghosh, S. Ray, B. Mishra and S. K. Tripathy, Phys. Rev. D 102, 024037 (2020)]. As a sequel in this paper, we substantially improve our previous model by choosing the Kuchowicz function as one of the metric potentials, which leads to many new interesting results and physical features from our analysis as discussed in this paper. Also, we provide essential additional stability checks on our gravastar model to investigate the possibility of any instability creeping in due to the higher-dimensional framework. Our present improved gravastar model is found to clear all the stability checks successfully. Very interestingly, the static spherically symmetric matter distributions are found to accommodate both classes of solutions obeying and violating the modified energy conditions on the RS brane as we find in this work. We can conclude from our analysis that the Kuchowicz metric potential is very effective for describing regular solutions to compact objects at substantially high energies on the three-brane. [ABSTRACT FROM AUTHOR]

We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding to a homogeneous space. What the gauging procedure amounts to is the construction of a Cartan geometry modelled on that Klein geometry, with the gauge field defining a Cartan connection. The lagrangian itself consists of all gauge-invariant top-forms constructed from the Cartan connection and its curvature. After demonstrating that this procedure produces four-dimensional General Relativity upon gauging Minkowski spacetime, we proceed to gauge all four-dimensional maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter-Carroll and the lightcone. For the first three of these spaces, our lagrangians generalise earlier first-order lagrangians. The resulting theories of carrollian gravity all take the same form, which seems to be a manifestation of model mutation at the level of the lagrangians. The odd one out, the lightcone, is not reductive and this means that although the equations of motion take the same form as in the other cases, the geometric interpretation is different. For all carrollian theories of gravity we obtain analogues of the Gauss-Bonnet, Pontryagin and Nieh-Yan topological terms, as well as two additional terms that are intrinsically carrollian and seem to have no lorentzian counterpart. Since we gauge the theories from scratch this work also provides a no-go result for the electric carrollian theory in a first-order formulation. [ABSTRACT FROM AUTHOR]

An f(R) gravity, where the Ricci scalar (R) term in the Einstein-Hilbert action of general relativity is generalised to its function f(R), is an alternative to a dark energy model to explain the current cosmic acceleration. In this paper the R-2 gravity, in which a term proportional to R-2 is added to the R term in the Einstein-Hilbert action, is explored in the Palatini approach. The results show that when the proportionality constant is negative, the R-2 gravity can give the de-Sitter universe, where the universe has the exponentially accelerating expansion, after the matter-dominated era without introducing dark energy. [ABSTRACT FROM AUTHOR]

In this paper, we examine the potential strong coupling problem at early times in a bouncing cosmological model with "strong gravity in the past" (Jordan frame), which is conformally related to inflation (Einstein frame). From naive-dimensional analysis in the Jordan frame, one would conclude that the quantum strong coupling energy scale can be lower than the classical energy scale. However, from the Einstein frame prospective, this should not be the case. We illustrate this point by calculation in the Jordan frame which shows cancellations of the dangerous contributions in the tree level amplitude. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that energy-momentum tensors defined by Einstein and Tolman in the general theory of relativity are same for any spacetime. It is also shown that in general theory of relativity, the Einstein super-potential α 0 ν and Tolman super-potential α 0 ν are different in general. Four different examples are also given to ensure the validity of our established statements. In all these examples, we observed that the values of the Einstein α 0 ν and Tolman α 0 ν super-potentials are different but the Einstein and Tolman energy-momentum distributions come out as same. All the results obtained in these four examples are consistent with the already obtained results in the literature. [ABSTRACT FROM AUTHOR]

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether's theorem and its converse. The relevance of General Relativity (GR) has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether's first theorem, an infinity of conserved energies-momenta (thus answering Schrödinger's 1918 false-negative objection). Second, Sean Carroll has asked (rhetorically) how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR (taking pseudotensor laws seriously). Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. [ABSTRACT FROM AUTHOR]

Measurements of the validity of General Relativity, as well as its effects in quantum mechanics, are becoming increasingly accessible to tabletop experiments. In this paper, we will introduce atomic clocks and explain the pathway to observing state-of-the-art gravitational redshift using atomic clocks, with the help of existing experimental examples. We will conclude with possible future directions. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the nonrelativistic level, there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a nonrelativistic limit of the Unruh effect. The symmetries of the associated Schrödinger equation are generated by the Newton–Hooke algebra, which arises from a nonrelativistic limit of a cosmological twistor space. [ABSTRACT FROM AUTHOR]

The paper re-examines the principal methodological questions, arising in the debate over the cosmological standard model's postulate of Dark Matter vs. rivalling proposals that modify standard (Newtonian and general-relativistic) gravitational theory, the so-called Modified Newtonian Dynamics (MOND) and its subsequent extensions. What to make of such seemingly radical challenges of cosmological orthodoxy? In the first part of our paper, we assess MONDian theories through the lens of key ideas of major 20th century philosophers of science (Popper, Kuhn, Lakatos, and Laudan), thereby rectifying widespread misconceptions and misapplications of these ideas common in the pertinent MOND-related literature. None of these classical methodological frameworks, which render precise and systematise the more intuitive judgements prevalent in the scientific community, yields a favourable verdict on MOND and its successors–contrary to claims in the MOND-related literature by some of these theories' advocates; the respective theory appraisals are largely damning. Drawing on these insights, the paper's second part zooms in on the most common complaint about MONDian theories, their ad-hocness. We demonstrate how the recent coherentist model of ad-hocness captures, and fleshes out, the underlying—but too often insufficiently articulated—hunches underlying this critique. MONDian theories indeed come out as severely ad hoc: they do not cohere well with either theoretical or empirical-factual background knowledge. In fact, as our complementary comparison with the cosmological standard model's Dark Matter postulate shows, with respect to ad-hocness, MONDian theories fare worse than the cosmological standard model. [ABSTRACT FROM AUTHOR]

This paper advances the state-of-the-art by extending the study of the analogy between the fabric of spacetime and elasticity. As no prior work exists about a potential spacetime thermal expansion coefficient α , we explore the analogy of general relativity with the theory of elasticity by considering the cosmological constant Λ as an additional space curvature of the structure of space due to a thermal gradient coming from the cosmic web and the cold vacuum and we propose ( α S Δ T e) 2 = (1 R 0 ) 2 = Λ with R 0 being the curvature radius of the space fabric. It follows from this analogy and from the supposed space model consisting of thin sheets of Planck thickness l p curved by this thermal gradient Δ T a possible thermal expansion coefficient of the equivalent elastic medium modeling the space α S = l p Λ Δ T of the order of α space-QFT = 1. 1 6 × 1 0 − 6 K − 1 . As spacetime and not only space must be considered in general relativity, this paper also proposes an innovative approach which consists in introducing into the interval ds2 of special relativity a temperature effect T : d s 2 = (1 ± α t T) 2 c 2 d t 2 − (1 ± α s T) 2 [ d x 2 + d y 2 + d z 2 ] (entropy variations correlated with time laps, based on temperature variations affecting always physically the clocks) based on different thermal expansion coefficients for space and time with for the flow of time t : c t c n τ = k B t n h × Δ T = α t Δ T. With T ≈ 106 K, n = 1 , the associate time interval is 4. 8 × 1 0 − 1 7 s and α t = 1. 0 × 1 0 − 6 K − 1 . The consequence of this hypothesis is that dark energy potentially becomes a thermal spacetime curvature ( α f T l p ) 2 with f equal to s or t depending of the temperature, the thermal entropy variation of the universe, the Planck thickness and time, that increases since the Big bang, depending on thermal expansion coefficients for spacetime α s and α t as a function, respectively, of Λ , k B h × t , in opposition to spacetime curvature gravity due to mass/energy density as described in general relativity. [ABSTRACT FROM AUTHOR]

This paper is intended to review the consequences of assuming tachyon scalar field as a candidate for dark energy from dynamical system technique and observational cosmology point of views. In the contexts of general relativity and teleparallel gravity, a variety of non-minimally coupled tachyon fields have been taken into consideration. These models provide us subclasses of scalar-tensor and scalar-torsion theories. This review covers the tachyonic chameleon, the non-minimally coupled tachyon field to the Gauss–Bonnet invariant and the tachyonic teleparallel dark energy models. Type Ia supernovae and baryonic acoustic oscillations datasets are the observational data that have been used to constrain the model parameters. [ABSTRACT FROM AUTHOR]

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered f (R) , f (R , T) and f (R , T , Q) theories (where R and T are the Ricci scalar and trace of the energy–momentum tensor, respectively, while Q = T a b R a b ) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories. [ABSTRACT FROM AUTHOR]

We show the stability of the geometric optics approximation in general relativity by constructing a family (g λ) λ ∈ (0 , 1 ] of high-frequency metrics solutions to the Einstein vacuum equations in 3 + 1 dimensions without any symmetry assumptions. In the limit λ → 0 this family approaches a fixed background g 0 solution of the Einstein-null dust system, illustrating the backreaction phenomenon. We introduce a precise second order high-frequency ansatz and identify a generalised wave gauge as well as polarization conditions at each order. The validity of our ansatz is ensured by a weak polarized null condition satisfied by the quadratic non-linearity in the Ricci tensor. The Einstein vacuum equations for g λ are recast as a hierarchy of transport and wave equations, and their coupling induces a loss of derivatives. In order to solve it, we take advantage of a null foliation associated to g 0 as well as a Fourier cut-off adapted to our ansatz. The construction of high-frequency initial data solving the constraint equations is the content of our companion paper (Touati in Commun Math Phys, 2023). [ABSTRACT FROM AUTHOR]

This study delves into the realm of solving Einstein's field equations within the framework of general relativity. In this paper, we present an exact solution derived through the vanishing complexity approach and offer a comparative analysis with the established embedding class one approach. This exploration sheds light on the efficacy and validity of these methods in generating solutions for Einstein's field equations. Our study involves a comprehensive exploration of several key parameters, encompassing thermodynamic factors, causality conditions, stability evaluations, as well as analyses of the mass function. Based on our findings, it can be suggested that the vanishing complexity approach could serve as a viable alternative method to the embedding class one approach for the derivation of exact solutions of Einstein's field equations. [ABSTRACT FROM AUTHOR]

In this paper, Ricci-inverse gravity is investigated. It is an alternative theory of gravity that introduces into the Einstein–Hilbert action an anti-curvature scalar that is obtained from the anti-curvature tensor which is the inverse of the Ricci tensor. An axially symmetric spacetime with causality violation is studied. Two classes of the model are discussed. Different sources of matter are considered. Then a direct relation between the content of matter and causality violation is shown. Our results confirm that Ricci-inverse gravity allows the existence of Closed Time-like Curves (CTCs) that lead to the violation of causality. Furthermore, a comparison is made between the results of general relativity and Ricci-inverse gravity. Other spacetimes, such as Gödel and Gödel-type universes, which are exact solutions of general relativity and allow for causality violations, are also explored in Ricci-inverse gravity framework. [ABSTRACT FROM AUTHOR]

For a hundred years, general relativity has been the best theory to describe gravity and space–time and has successfully explained many physical phenomena. At the same time, quantum mechanics provides the most accurate description of the microscopic world, and quantum science technology has evoked a wide range of developments today. Merging these two very successful theories to form a grand unified theory is one of the most elusive challenges in physics. All the candidate theories that wish to unify gravity and quantum mechanics predict the breaking of the weak equivalence principle, which lies at the heart of general relativity. It is therefore imperative to experimentally verify the equivalence principle in the presence of significant quantum effects of matter. Cold atoms provide well-defined properties and potentially nonlocal correlations as the test masses and will also improve the limits reached by classical tests with macroscopic bodies. The results of rigorous tests using cold atoms may tell us whether and how the equivalence principle can be reformulated into a quantum version. In this paper, we review the principles and developments of the test of the equivalence principle with cold atoms. The status of the experiments and the key techniques involved are discussed in detail. Finally, we give an outlook on new questions and opportunities for further exploration of this topic. [ABSTRACT FROM AUTHOR]

This paper studies the motion of a light signal and a test particle in the field of an infinite flat slab in terms of the general theory of relativity. The two cases of an external solution for a gravitational field in a vacuum corresponding to Rindler and Taub metrics are examined. The time of the motion and the path traveled by a particle before it stops are determined. It is shown that in the Taub geometry, as opposed to a light signal, a material particle does not reach a singularity. The minimum distance from the singularity is determined as a function of the particle energy. Results in terms of the special theory of relativity are given for comparison. [ABSTRACT FROM AUTHOR]

In this paper, we exhibit analytical solutions for the evolution of the mass of an astrophysical object accreting cosmic fluid according to the Bondi–Hoyle–Lyttleton mechanism. The key assumption of this model is that the adiabatic speed of sound within the accreted fluid directly affects the rate of change of the mass of the accreting object. We consider different literature equations of state, as the (Modified) Berthelot, Logotropic, generalized polytropic of index n, and quadratic models. We assume the fluid to evolve either according to General Relativity or to the Randall-Sundrum type 1 gravity model far away from the astrophysical object in an asymptotically Friedman universe. We claim that this accretion mechanism is unlikely to affect the mass-radius relationship of the photon sphere beyond the Schwarzschild one at the present time, and that the critical point of accretion in the (Modified) Berthelot fluid flow is hidden by the event horizon. Our work belongs to the broader research line investigating the interplay of small-scale and large-scale Physics in the modeling of gravitational phenomena. [ABSTRACT FROM AUTHOR]

Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the New-tonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unraveled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic. [ABSTRACT FROM AUTHOR]

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing Riemannian curvature. Moreover, we obtain equivalent conditions for locally Minkowski Finsler warped product spaces. Finally, we explicitly construct two types of non-Riemannian examples. [ABSTRACT FROM AUTHOR]

This paper proposes a theoretical study that investigates quantum effects on the gravity of black holes. This study utilizes a gravitational model that incorporates quantum mechanics derived from the classical-like quantum hydrodynamic representation. This research calculates the mass density distribution of quantum black holes, specifically in the case of central symmetry. The gravity of a quantum black hole shows contributions coming from quantum potential energy, which is also sensitive to the presence of a background of gravitational noise. The additional energy, stored in quantum potential fluctuations and constituting a form of dark energy, leads to a repulsive gravity in the weak gravity limit. This repulsive gravity overcomes the attractive classical Newtonian force at large distances of order of the intergalactic length. [ABSTRACT FROM AUTHOR]

In this paper, we investigate almost Schouten solitons and almost gradient Schouten solitons in spacetimes of general relativity. At first, it is proven that if a generalized Robertson–Walker spacetime permits an almost Schouten soliton, then it becomes a perfect fluid spacetime as well as the spacetime represents a dark matter era. Besides this, we investigate almost gradient Schouten solitons in generalized Robertson–Walker spacetimes. Moreover, a spacetime obeying almost Schouten solitons whose potential vector field is a non-homothetic conformal vector field is of Petrov type O or N. [ABSTRACT FROM AUTHOR]

Kim and Lee [Phys. Rev. D 63 (2001) 064014] studied charged wormholes and Morris–Thorne wormholes in the presence of scalar field using the concepts of general relativity. In this paper, we have also considered same wormholes affected with electric charge and scalar field and extended their study using the framework of f (R , T) gravity with f (R , T) = R + β R 2 + λ T gravity model, where β and λ are constants. We have examined the possibility for minimization of the amount of exotic matter through energy conditions. Further, we have obtained the deflection angle, an important notion in gravitational lensing, by using strong field limit coefficients which may be helpful in the detection of wormholes. [ABSTRACT FROM AUTHOR]

The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we find differential equations of Finsler warped product metrics with vanishing χ -curvature or vanishing H-curvature. Furthermore, we show that, for Finsler warped product metrics, the χ -curvature vanishes if and only if the H-curvature vanishes. [ABSTRACT FROM AUTHOR]

In the literature different concepts of compatibility between a projective structure P and a conformal structure C on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than compatibility in the Riemannian sense. In an often cited paper (Ehlers et al. in: O'Raifertaigh (ed) General Relativity, Papers in Honour of J.L. Synge, Clarendon Press, Oxford, 2012) Ehlers/Pirani/Schild introduce still another criterion which is natural from the physical point of view: every light like geodesics of C is a geodesics of P . Their claim that this type of compatibility is sufficient for introducing a Weylian metric has recently been questioned (Trautman in Gen Relativ Gravit 44:1581–1586, 2012); (Vladimir in Commun Math Phys 329:821–825, 2014); as reported by Scholz (in: A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection, 2019). Here it is proved that the conjecture of EPS is correct. [ABSTRACT FROM AUTHOR]

In this methodological paper, we consider two problems an astronaut faces under the black hole horizon in the Schwarzschild metric. (1) How to maximize the survival proper time. (2) How to make a visible part of the outer universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the "river model." Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point (1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point (2) requires maximizing the peculiar velocity of the observer. Both goals (1) and (2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology and its application for the problems studied in this paper can be used in advanced general relativity courses. [ABSTRACT FROM AUTHOR]

In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture $$\displaystyle \sigma =0 {\displaystyle \, =>}\, {\displaystyle \omega }\,{\displaystyle \varTheta } =0$$ by Senovilla et al. (Gen. Relativ. Gravit 30:389-411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at . We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory. [ABSTRACT FROM AUTHOR]

This paper considers the relationship between electromagnetic waves and the geometric optics approximation in general relativity. The approximation is widely used in predictions of observations in astronomy and cosmology, for example in gravitational lensing and the cosmic microwave background. Its properties are thus of considerable significance. The paper's author was a Golden Oldies board member and a prominent author and editor for Springer. It complements other Golden Oldies by Ehlers showing the importance and influence of his attention to issues concerning the relation of exact physical theories and their approximations. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated magnetized Bianchi type-VI0 string cosmological model for antistiff fluid in general relativity. We assume that F23 is the only survival component of electromagnetic field tensor Fij. For the absolute determination of the model, we assume the expansion in the model is proportional to the shear. The common measures of the Einstein's field equations for the cosmological model have been acquired under the assumption of anti-stiff fluid i.e. p + ρ = 0, where ρ and p are the rest energy density and the pressure of the fluid, respectively. The physical and geometrical outcomes of the model in the presence of magnetic field are discussed. [ABSTRACT FROM AUTHOR]

We develop a new approach to find asymptotic symmetries in general relativity as a modification of the Lie-algebra-based approach proposed in T. Tomitsuka et al. [Classical Quantum Gravity 38 , 225007 (2021)]. Those authors proposed an algorithmic protocol to investigate asymptotic symmetries. In particular, their guiding principle helps us to find a non-vanishing charge that generates an infinitesimal diffeomorphism. However, in order to check the integrability condition for the charges, it is necessary to solve differential equations to identify the integral curve of vector fields, which is usually quite hard. In this paper, we provide a sufficient condition of the integrability condition that can be checked without solving any differential equations, avoiding the difficulties in the approach in the above reference. As a demonstration, we investigate the asymptotic symmetries on a Killing horizon and find a new class of asymptotic symmetries. In 4D spacetimes with a spherical Killing horizon, we show that the algebra of the corresponding charges is a central extension of the algebra of vector fields. [ABSTRACT FROM AUTHOR]

Inspired by high-energy physics and by considering standard gravity theory as the low-energy limit of quantum theory, the modification of general relativity as R + f (G) has been proposed. This paper is dedicated to investigating the cosmological model of modified Gauss–Bonnet gravity in four dimensions. General field equations for the four-dimensional Friedmann– Robertson–Walker metric are given in detail. Also, it is well known that Hubble parameter H (z) measurements are helpful for the inference of cosmological model parameters. We try to explain the MCMC statistical approach used to calculate Hubble's parameter. The resulting form of H (z) was limited using Cosmic Chronometric data, Standard Candles SN Ia from Pantheon, and Baryon Acoustic Oscillations to obtain the best match values by using the regression equation. Finally, to examine the late-time dynamics of our Universe, the behavior of physical and kinematic variables like the deceleration parameter (q) , State-finder parameters { r , s } , diagnostic parameter ( O m (z)), equation of state parameter as well as the behavior of energy conditions versus redshift with the parameter values are presented. [ABSTRACT FROM AUTHOR]

Biquaternion algebra is an algebraic structure originating from a complex number and has mainly been used in quantum mechanics, special and general relativity, classical, relativistic, and covariant electrodynamics, and signal processing. In this paper, the problem of the diagonalization of a biquaternion matrix is studied, by means of a complex representation of a biquaternion matrix, and an algebraic algorithm for the diagonalization of a biquaternion matrix is presented. In addition, numerical examples demonstrate the effectiveness of the algebraic algorithm. [ABSTRACT FROM AUTHOR]

General theory of relativity can be equivalently formulated on a flat spacetime associating a torsion-free affine connection of non-vanishing non-metricity scalar Q. In this paper, we present an extension of this, viz., the f (Q) theory of gravity, and explore the early evolution of the universe in the background of anisotropic Bianchi-I model. The f (Q) theory in the current setting through its geometric modification is quite successful in explaining the late time accelerated expansion. Here, we note that it accommodates latest released constraints on the inflationary parameters by Planck's collaboration group with excellent precession, but fails to produce a viable decelerated expansion in the radiation dominated era. [ABSTRACT FROM AUTHOR]

In this paper we investigate the impact of lensing magnification on the analysis of Euclid's spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead. [ABSTRACT FROM AUTHOR]

This paper is devoted to observe the physical attributes of isotropic relativistic spherical objects in the context of Rastall theory of gravity. In order to inspect the structural composition of spherical objects, the Tolman IV solution is taken into account. The unknown parameters associated with Tolman IV solution are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition and stellar equation for several choices of Rastall parameter. It is observed that the considered solution does not admit singularities in the matter variables. Moreover, in accordance with the graphical analysis, the stellar models satisfy all physical requirements anticipated in a realistic star. It is also shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved. [ABSTRACT FROM AUTHOR]

This paper focuses on the Einstein–Cartan theory, an extension of general relativity that incorporates a torsion tensor into spacetime. The differential form technique is employed to analyze the Einstein–Cartan theory, which replaces tensors with tetrads. A tetrad formalism, specifically the Newman–Penrose–Jogia–Griffiths formalism, is used to study the field equations. Also, the energy–momentum tensor is determined, considering a Weyssenhoff fluid with anisotropic matter. The spin density is derived in terms of the redshift function. Additionally, our findings demonstrate that the radial sound speed within the wormhole throat exceeds the speed of light, suggesting the existence of superluminal matter, while the tangential sound speed indicates near-light-speed propagation, particularly within the throat, emphasizing the significance of exotic matter in comprehending wormhole properties. The results also extend to examining the energy conditions at the throat of a Morris–Thorne wormhole, shedding light on the properties of wormholes within the context of the Einstein–Cartan theory, including the energy conditions at the throat. [ABSTRACT FROM AUTHOR]

We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H 0 tension. [ABSTRACT FROM AUTHOR]

The contribution to the correction of the perihelion precession of binary systems due to energy loss from gravitational radiation emissions, as a follow-up to our previous papers, is obtained for the OJ287 system, which has a large discrepancy not satisfied by the Schwarzschild metric. Using our formulation of the perihelion advance correction from the rate of change of the orbital energy, as well as our alternate correction and spin contributions from previous papers, we obtain a theoretical value of 39.76 degrees for the total perihelion precession angle correction of the OJ287 system, within 1.7% of the observed value of 39.1 ± 0.1. [ABSTRACT FROM AUTHOR]