Einstein's Theory Of Gravitation Research Articles

Multicollinear singularities in celestial CFT

The purpose of this paper is to study the holomorphic multicollinear limit of (celestial) amplitudes and use it to further investigate the double residue condition for (hard celestial) amplitudes and the celestial operator product expansion. We first set up the notion of holomorphic multicollinear limits of amplitudes and derive the 3-collinear splitting functions for Yang-Mills theory, Einstein gravity, and massless ϕ3 theory. In particular, we find that in ϕ3 theory the celestial 3-OPE contains a term with a branch cut. This explicit example confirms that branch cuts can obstruct the double residue condition for hard celestial amplitudes, which is the underlying cause of the celestial Jacobi identities not holding for certain theories. This addresses an ongoing debate in the literature about associativity of the celestial OPEs and concretely demonstrates a new (multi-particle) term in the celestial OPE coming from the multi-particle channel in the amplitudes.

Asymptotic Weyl double copy in Newman-Penrose formalism

In this paper, we provide a self-contained investigation of the Weyl double copy in the Newman-Penrose formalism. We examine the Weyl double copy constraints for the general asymptotically flat solution in the Newman-Unti gauge. We find that two transparent solutions of the asymptotic Weyl double copy constraints lead to truncated solutions for both linearized and Einstein gravity theory where the solutions are in the manifest form of Petrov type N or type D in the Newman-Unti gauge.

The Descartes Code (Spin Orbital Rotation of Photons)–II. The Gravitational Redshift

A new alternative model to the Schwarzschild’s solution of the Einstein's gravitational theory is presented. Descartes’s code is the old color theory (published in 1637) based on the rotation of “light globules”, however, it was rejected by Newton in 1672. In this model, the photon spin-orbital speed is modified by the gravitational field. The formulae for the wavelength, frequency, local time, momentum, energy, and temperature of photons in the gravitational field are identical in the first order both for the Schwarzschild solution and Descartes’ code. To experimentally determine the predictions of Descartes’ photon model we have to search for the experiments in the second order or for the situations where the standard model has to postulate some hidden elements (e.g., the dark matter). Some examples are presented here. The new interpretations of the bending of light by the Sun and the Shapiro time delay are given. The Anderson acceleration constant known as the Pioneer anomaly was derived as the effect of the Earth’s gravitational field on photons. Similar acceleration could be found in invaluable data from the Laser Lunar Ranging experiment. Stellar photons are modified by the Solar gravitational field at the distance of 1 AU and the acceleration constant identical to the Milgrom acceleration (MOND gravitational model) was derived. Therefore, we should study in more detail the influence of the Solar, Earth’s, and Moon’s gravitational fields on photons to avoid traps with false gravitational models.

Constraining Snyder and GUP models with low-mass stars

We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behaviour of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is β0≤4.5×1047\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _0 \\le 4.5 \ imes 10^{47}$$\\end{document}. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

A new slow-rotating black hole solution in Chern-Simons axion of Einstein gravity

This research aims to incorporate an axionic field within the context of dynamical Chern-Simons (CS) gravity and investigate the behavior of a slowly rotating black hole (BH) within this theoretical framework. To the best of our knowledge, this is the first instance where such a problem has been tackled within the context of (CS) gravitational theory coupled with the axionic field. The Lagrangian of this theory includes two CS scalar field functions, denoted as ω(ϑ) and U(ϑ), where ϑ represents the CS scalar field. Our investigation involves calculating the equation related to the CS scalar field and demonstrating that deriving a solution necessitates imposing constraints on U and ω, specifically in the form of U′=ω, where U′≡dU(ϑ)dϑ. By utilizing the solution for the CS scalar field in other field equations, we reveal that the enigmatic function U can be expressed explicitly as U=ϑ2p+1, where p represents an integer with unrestricted values. In the instance where p=0, the CS Axion Einstein gravity theory [1] aligns with the study carried out in [2]. Furthermore, our analysis establishes that for positive values of p, the theory is capable of generating a significantly potent CS BH compared to the model derived in [2]. Moreover, our study delves into the geodesics of this BH, deriving its conserved quantities, orbital period, as well as its geodesic precession angle.

Holographic complexity of rotating black holes with conical deficits

Based on the complexity equals action (CA) and complexity equals volume (CV) conjectures, we investigate the holographic complexity of a slowly accelerating Kerr-AdS black hole in the bulk Einstein gravity theory which is dual to holographic states with rotation and conical deficits in the boundary quantum system. Upon obtaining an implicit form of the Wheeler-DeWitt patch, we evaluate the action and show that the growth rate of the CA complexity violates volume-scaling formulation in large black hole limit due to the non-trivial contribution from the not-too-small acceleration of the black hole. Moreover, in an ensemble with fixed entropy, pressure, and angular momentum, we also find that complexity of formation decreases with both the average and difference of the conical deficits on the poles when the black hole is close to the static limit but increases with the deficits when the black hole is close to the extremal regime.

Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory

The dynamical evolution of the Hajicek $1$-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory of gravity, the evolution equation is related to a projected part of the Einstein tensor $(\hat{G}_{ab})$ on a generic null surface $\mathcal{H}$, particularly $\hat{G}_{ab}l^a q^b_{~c}$, where $l^a$ and $q^a_{~c}$ are the outgoing null generators of $\mathcal{H}$ and the induced metric to a transverse spatial cross-section of $\mathcal{H}$ respectively. Under the {\it geodesic constraint} a possible fluid interpretation of this evolution equation is then proposed. We find that it has the structure which is reminiscent to the {\it Cosserat generalization} of the Navier-Stokes fluid provided we express the dynamical evolution equation of the Hajicek $1$-form in a set of coordinates adapted to $\mathcal{H}$ and in a local inertial frame. An analogous viewpoint can also be built under the motive that the usual material derivative for fluids should be replaced by the Lie derivative. Finally, the tidal force equation in EC theory on the null surface is also derived.

U(1) CS theory vs SL(2) CS formulation: Boundary theory and Wilson line

We first derive the boundary theory from the U(1) Chern-Simons theory. The boundary action on an n-sheet manifold appears from its back-reaction of the Wilson line. The reason is that the U(1) Chern-Simons theory can provide an exact effective action when introducing the Wilson line. The Wilson line in the pure AdS3 Einstein gravity is equivalent to entanglement entropy in the boundary theory up to classical gravity. The U(1) Chern-Simons theory deviates by a self-interaction term from the gauge formulation on the boundary. We also compare the Hayward term in the SL(2) Chern-Simons formulation to the Wilson line approach. Introducing two wedges can reproduce the entanglement entropy for a single interval at the classical level. We propose quantum generalization by combining the bulk and Hayward terms. The quantum correction of the partition function vanishes. In the end, we calculate the entanglement entropy for a single interval. The pure AdS3 Einstein gravity theory shows a shift of central charge by 26 at the one-loop level. The U(1) Chern-Simons theory does not show a shift from the quantum effect. The result is the same in the weak gravitational constant limit. The non-vanishing quantum correction shows that the Hayward term is incorrect.

Development and perspectives of relativistic astrophysics in Uzbekistan

Speedy advancement in research in Astrophysics and related area around the globe has led scientists in Central Asia to produce high-quality research and constitute strong research in Relativistic Astrophysics and the Einstein theory of gravitation. Consequently, immense impact of this progress has been seen in central Asian countries in not only in research in Astrophysics and related areas, the academic institutions also received a trickle down effect in terms of the advancement in teaching as well as research. This focus of this paper is to overview the research incentives that are being taken up by the Theoretical Astrophysics Group located at Ulug Beg Astronomical Institute of Uzbekistan Academy of Sciences, Tashkent.

Bound on the rate of Bondi mass loss

To ensure the light (emitted far away from the source of gravity) can arrive at the null infinity of an asymptotically flat spacetime, it is shown that the rate of Bondi mass aspect has to satisfy some conditions. In Einstein gravity theory, we find the sufficient condition implies a bound on the Bondi mass $m$, i.e., $|\dot{m}|\leqslant 0.3820~c^3/G$. This provides a new perspective on Dyson's maximum luminosity. However, in Brans-Dicke theory, the sufficient condition depends on the behavior of the radiation field of the scalar. Specifically, the photons can escape to the null infinity when the scalar gravitational radiation is not too large and the mass loss is not too fast.

Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble

In the context of Black Hole Chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics are discussed in the grand canonical (fixed $U(1)$ potential, $\Phi$) ensemble. Considering all higher-order graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, exact TBH solutions are derived, the explicit form of the on-shell action is computed, and the associated thermodynamic quantities in the Grand Canonical Ensemble (GCE) are calculated. In addition, the validity of the first law of thermodynamics and Smarr relation are examined in the extended phase space. Regarding this model, it is shown that a van der Waals (vdW) behavior takes place in $d \ge 4$ dimensions, a typical reentrant phase transition is observed in $d \ge 5$, and both anomalous vdW and triple point phenomena are recognized in $d \ge 6$. So, the results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Besides, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a special subgroup of our solutions for both Einstein and massive gravity theories in various ensembles.

Kaluza–Klein Universe interacting with wet dark fluid in f(R,T) gravity

In this paper, we study the essence of [Formula: see text] gravitation theory in five-dimensional Universe and see the role of dark energy in the form of wet dark fluid in a Kaluza–Klein Universe. It is found that the dark energy is not exaggerated in contributing to the accelerating expansion of the Universe though the expansion is inherent as a result of the theory itself and due to the geometric contribution of matter. It is interesting to see that in some model it is found that there was some era before the beginning of the present era. Some of the models are seen to go to [Formula: see text]CDM models in late future as in Einstein gravitation theory, starting the evolution with a big bang. Most of the models undergo early inflation as well as late-time accelerating expansion thus defining as good models for real astrophysical situations, with dark energy playing fundamental role in these Universe. Most interesting observation from this investigation is that we can developed new isotropic and anisotropic models of Kaluza–Klein Universe.

Chern–Simons extension of ESK theory

The commonly-known Chern-Simons extension of Einstein gravitational theory is written in terms of a square-curvature term added to the linear-curvature Hilbert Lagrangian. In a recent paper, we constructed two Chern-Simons extensions according to whether they consisted of a square-curvature term added to the square-curvature Stelle Lagrangian or of one linear-curvature term added to the linear-curvature Hilbert Lagrangian [Ref. 4]. The former extension gives rise to the topological extension of the re-normalizable gravity, the latter extension gives rise to the topological extension of the least-order gravity. This last theory will be written here in its torsional completion. Then a consequence for cosmology and particle physics will be addressed.

The most complete mass-dimension four topological gravity

The usual Chern-Simons extension of Einstein gravity theory consists in adding a squared Riemann contribution to the Hilbert Lagrangian, which means that a square-curvature term is added to the linear-curvature leading term governing the dynamics of the gravitational field. However, in such a way the Lagrangian consists of two terms with a different number of curvatures, and therefore not homogeneous. To develop a homogeneous Chern-Simons correction to Einstein gravity we may, on the one hand, use the above-mentioned square-curvature contribution as the correction for the most general square-curvature Lagrangian, or on the other hand, find some linear-curvature correction to the Hilbert Lagrangian. In the first case, we will present the most general square-curvature leading term, which is in fact the already-known re-normalizable Stelle Lagrangian. In the second case, the topological current has to be an axial-vector built only in terms of gravitational degrees of freedom and with a unitary mass dimension, and we will display such an object. The comparison of the two theories will eventually be commented.

Study on anisotropic stars in the framework of Rastall gravity

We investigate the existence of high dense compact objects in the light of Rastall gravity theory. The material content is driven by an imperfect fluid distribution and the inner geometry is described by the Tolman–Kuchowicz space–time. The validity of the obtained model is checked by studying the main salient features such as energy–density, radial and tangential pressures and anisotropy factor. Since Einstein gravity theory shares the same vacuum solution with Rastall gravity theory, the interior geometry is joining in a smoothly way with the exterior Schwarzschild’s solution. The equilibrium of the model under different gradients is analyzed by using the modified hydrostatic equilibrium equation, containing the so–called Rastall gradient. The compact structure has a positive anisotropy factor which enhances the balance and stability mechanisms. To check the potentially stable behavior, we employ Abreu’s and adiabatic index criterion. It was found that the model is completely stable. The incidence of the Rastall’s parameter $\gamma $ on all the physical quantities that characterize the model is described by the help of graphical analysis. Concerning the $\gamma $ spectrum we have considered $0.3142\leq \gamma \leq 0.3157$ . All the results are compared with the general relativity case.

Lattice AdS geometry and continuum limit

We construct the lattice AdS geometry. The lattice AdS2 geometry and AdS3 geometry can be extended from the lattice AdS2 induced metric, which provided the lattice Schwarzian theory at the classical limit. Then we use the lattice embedding coordinates to rewrite the lattice AdS2 geometry and AdS3 geometry with the manifest isometry. The lattice AdS2 geometry can be obtained from the lattice AdS3 geometry through the compactification without the lattice artifact. The lattice embedding coordinates can also be used in the higher-dimensional AdS geometry. Because the lattice Schwarzian theory does not suffer from the issue of the continuum limit, the lattice AdS2 geometry can be obtained from the higher-dimensional AdS geometry through the compactification, and the lattice AdS metric does not depend on the angular coordinates, we expect that the continuum limit should exist in the lattice Einstein gravity theory from this geometric lattice AdS geometry. Finally, we apply this lattice construction to construct the holographic tensor network without the issue of a continuum limit.

Quantum correction of the Wilson line and entanglement entropy in the pure AdS3 Einstein gravity theory

We calculate the expectation value of the Wilson line in the pure AdS3 Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of “minimum surface=entanglement entropy”.

On the metrizability of the affine connectivity space and the unified theory of fundamental interactions

We propose the background connectivity interpret as the empirical connectivity, received as the particular case of the transition operator, which had been by induced by the collision integral. Approximating the transition operator by the differential operator we shall demand minimum variance of the given operator from the transition operator for the definition of the metric tensor. As a result we receive with the help of the variation formalism the differential equation of the regression, solving of which can find the metric tensor. By the help of the given tensor we receive the Christoffel symbols. Using the metric tensor and the Christoffel symbols can construct both the Einstein gravitation theory and the Chernikov gravitation theory with the two connectivity’s. Constructing the empirical connectivity theory we shall use the generalized functions, that implies the change of the space-time topology.

Anisotropic fluid spheres in the framework of [formula omitted] gravity theory

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f(R,T) scenario. To do so we use modified Durgapal–Fuloria metric potential and the pressure anisotropy condition is imposed in order to obtain the effective anisotropic factor Δ̃. Besides, a notable and viable election on f(R,T) gravity formulation is taken. The choice of f(R,T) function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, pressure, subliminal speeds of sound, surface redshift etc. We analyze all the physical and mathematical general requirements of the configuration taking M=1.04M⊙ and varying χ from −0.1 to 0.1. It is shown by the graphical procedure that χ<0 yields a more compact object in comparison when χ≥0 (where χ=0.0 corresponds to general relativity) and increases the value of the surface redshift. However, negative values of χ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu’s criterion). Furthermore, the model in Einstein gravity theory presents cracking while for χ>0 the system is fully stable. The relationship between effective radial pressure p̃r and effective density ρ̃ is discussed and obtained. This is achieved by establishing the corresponding equation of state.

On a Generalization of the Einstein Gravitational Equations Based on Weyl Geometry

In the recent years, the interest in modifications of the Einstein theory of gravitation has seriously increased due to the unsolved problem of dark energy. One of them was suggested in our earlier publications where a generalization of the Einstein gravitational theory with Weyl’s connection was studied. In the generalization, the Weyl vector potentials were regarded as a weak field giving small corrections to the Einstein gravitational equations and which could be associated with dark energy. However, in these publications only uncharged dustlike matter was considered as a source of gravitation. In the present paper, we consider the generalized Einstein gravitational equations with Weyl’s connection in the important case in which gravitation is caused by charged matter consisting of particles interacting by means of gravitational and electromagnetic forces. In Weyl’s theory and in a number of other gravitational theories based on Weyl’s geometry, gauge-invariant Lagrangians of second order in the curvature were used, which gave gravitational equations of fourth order in the derivatives of the metric, in contrast to the second order of the Einstein equations. That is why we choose another way to investigate the Einstein gravitational equations with Weyl connection. We study the consequences of our equations and obtain conditions of their consistency. Using these conditions, we come to second-order differential equations for the Weyl vector field and to generalized dynamic equations for charged matter.