Momentum Tensor Research Articles

Gravastars in f ( R , G , T ) gravity

The article examines the matter of gravitational vacuum stars, or gravastars, in the context of [Formula: see text] gravity, where [Formula: see text], [Formula: see text], and [Formula: see text] refer to the Ricci Scalar, Gauss–Bonnet invariant term, and trace of energy–momentum tensor, respectively. Here, using certain suitable numerical approaches, solutions to the highly nonlinear differential equations are determined. For a well-known [Formula: see text] gravity cosmological model, the main structure of gravastars has been discussed according to core, shell, and external region. It is illustrated graphically how the relationship between mass and radius has evolved for the gravastar under consideration.

Anisotropic extensions of Tolman IV through decoupling in energy–momentum squared gravity

This paper is dedicated to the precise computation of anisotropic extensions for the Tolman IV solution. These extensions are achieved through the utilization of the extended gravitational decoupling scheme within the framework of [Formula: see text] gravity, where R is the Ricci scalar and [Formula: see text] is the contraction of energy–momentum tensor. In this context, we select a linear model characterized by the expression [Formula: see text], where the parameter [Formula: see text] establishes a connection between the geometric and matter components. The extended gravitational decoupling technique incorporates a decoupling parameter that governs the extent of the induced anisotropy. Deformations in the radial and temporal metric components lead to the decomposition of the field equations into two distinct subsystems. One of these sets pertains to the isotropic solution, while the other is addressed by implementing the extra constraints. We examine the outcomes through graphical analysis and investigate the viability and stability of the obtained anisotropic solutions for the celestial object. Moreover, we study the mass, compactness and surface redshift of the system to gain a comprehensive understanding of its characteristics. It is concluded that this technique in this modified gravity yields physically acceptable solutions.

Chronology Protection in f(T) Gravity: The Case of Gott’s Pair of Moving Cosmic Strings

As a consequence of the spacetime structure, defined by the tetrad field instead of the metric tensor alone, f(T) gravity seems to harbor its own chronology protection agency. When Gott’s pair of moving cosmic strings is considered, it is shown that the requirement of having a global parallelization—i.e., a global smooth field of tetrads– drastically restricts the form of the tetrads on the junction surface between the two strings. The junction conditions on the tetrad field are satisfied only if the corresponding boosts needed to put the strings in motion are null on the matching surface. This seems to throw overboard Gott’s construction from the outset without the need for analyzing the divergence of the expectation value of the energy–momentum tensor on the Cauchy horizon, evading in this way bothersome quarrels concerning the choice of vacuum.

Electromagnetic extension of Buchdahl bound in f(R, T) gravity

We develop a static charged stellar model in f(R, T) gravity where the modification is assumed to be linear in T which is the trace of the energy momentum tensor. The exterior spacetime of the charged object is described by the Reissner–Nordström metric. The interior solution is obtained by invoking the Buchdahl–Vaidya–Tikekar ansatz, for the metric potential grr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{rr}$$\\end{document}, which has a clear geometric interpretation. A detailed physical analysis of the model clearly shows distinct physical features of the resulting stellar configuration under such a modification. We find the maximum compactness bound for such a class of compact stars which is a generalization of the Buchdahl bound for a charged sphere described in f(R, T) gravity. Our result shows physical behaviour that is distinct from general relativity.

Late time cosmological solutions in f(R,T) gravity in a viscous universe

Considering the condition on conservation of energy–momentum tensor (EMT), we study late time cosmological solutions in the context of [Formula: see text] gravity (where [Formula: see text] and n are constants) in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. The present model discusses the case of a barotropic perfect fluid as the matter content of the Universe, along with the case when dissipative effects are taken into account. Briefly, assuming a single perfect fluid, we find that the mentioned model is not capable of presenting an observationally consistent picture of the late time accelerated expansion of the Universe; nevertheless, the model leads to admissible solutions when the bulk viscosity is included. In this regard, a consistent setting is found considering the Eckart, Truncated and Full Israel–Stewart theories which determine the behavior of bulk viscosity. In the presence of bulk viscosity, the behavior of the deceleration parameter (DP) shows that the underlying model can describe an acceptable evolution even if the isotropic pressure of matter content of the Universe is negligible.

Measures of Distance in Quantum Mechanics

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental.

Физическое состояние объектов прошлого и будущего

The theory of absolute space-time, on which the theory of relativity is based, thanks to Minkowski, says that the events of the past, present and future are equal in relation to their existence, i.e. they always exist and never disappear. The article examines the question of the physical state of their existence. A formalism is being built within the framework of the Relativity theory, according to which, since we do not see or interact with objects of the past and future, their states represent the socalled ghostly matter, characterized by a zero energy- momentum tensor. With the passage of coordinate (global) time, ghostly matter passes into the present and is discovered as reality, and then again passes into ghostly and becomes an object of the past.

Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String

In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.

Bianchi Type V Cosmological Scenario In f(R,T) Gravity Theory With Special Form Of Scale Factor

In this study, we have examined the exact solutions of the field equations for a Bianchi type V universe filled with bulk viscous fluid within the framework of theory, where and and represent the Ricci scalar and the trace of the energy momentum tensor, respectively. We used a combination of exponential and hyperbolic scale factors to determine the physical parameters and metric potentials in the space-time. We also investigated the geometrical and physical parameters of the model, as well as the energy conditions. Additionally, we found that the state finder diagnostic pair falls within an acceptable range.

Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.

Non-minimal unimodular inflation

We study an extension of the unimodular cosmological inflation in the context of the non-minimal coupling of a generic scalar field with gravitational sector. We consider the non-minimal coupling of the scalar field and gravity as the only source of energy–momentum tensor in this setup. Without introducing new particles other than those already existing in electroweak theory, the generic scalar field’s non-minimal coupling is responsible for the generation of the seeds of perturbations for structure formation and the observed Cosmic Microwave Background anisotropies in this scenario. We calculate inflation parameters in both the Jordan and Einstein frames, and then we study primordial spectral indices for slow-roll parameters in Einstein’s frame at the first and second orders. The numerical results of this model are consistent with the Planck2018 and BICEP/Keck joint data sets in some subspaces of the model parameters space. By considering a sufficient amount of inflation, we estimate the strength of the non-minimal coupling parameter, ξ, to find appropriate new constraints on the values of this parameter. By comparing the numerical values of the inflation observables in two frames and also with observation, we comment on the issue of frames in this framework.

What is a real black hole?

Abstract Four dimensional Einstein equation with non-vanishing energy momentum tensor is solved to give a solution where the event horizon of a celestial body is outside of the body, which corresponds to a black hole by definition. There is no singularity at the center of the object unlike the case of Schwarzschild solution. We do not have the gravitational collapse. We do not have the gravitational collapse thus avoiding the Penrose-Hawking singularity theorems. The main feature of our black hole solution is that it has the horizon inside the black hole in addition to the usual outside horizon. This inner horizon singularity is not removable by a coordinate transformation because the determinant of metric tensor is singular at this point but there is no singularity neither in the density nor in the pressure indicating there is no gravitational collapse.

More on the fact that Rastall = GR

Rastall gravity is the same as General Relativity, with a simple algebraic redefinition of what is called the energy–momentum tensor. Despite it having been very clearly explained by M. Visser several years go, there are still many papers claiming big differences between the two formulations of gravitational equations and trying to use them for problems of physics. When going this way, the totally ignored task is to explain why the conserved energy–momentum quantities and the quantities used for other purposes are different from each other. Moreover, when researchers are using the non-conserved energy density and pressure for determining the sound speed, it is just inconsistent with the Rastall gravity. I carefully explain all this, and also show how one could construct a variational principle for producing equations in the Rastall form.

On curvature related geometric properties of Hayward black hole spacetime

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F⋅F=LQ(g,F) for F=W,C,K with a smooth scalar function L), and it also possesses the relation R⋅R−LQ(g,C)=Q(S,R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η-Ricci soliton as well as an almost η-Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc.

Axially symmetric exponential metric

We present a new family of vacuum axially symmetric static solutions to Einstein’s field equations. This solution is a geometrically modified version of the Yilmaz exponential metric (YEM) which has recently been shown to represent a traversable wormhole. This vacuum solution is a one-parameter static singular solution with its singularity located at r=0. Furthermore, it is shown that both the YEM and its geometrically modified version, introduced in this work i.e., the Axially Symmetric Exponential metric (ASEM) belong to a general 2-parameter class of solutions supported by an anisotropic fluid. Depending on the parameters the generic energy–momentum tensor represents either an exotic or a normal fluid. Concerning the ASEM, the circular stable orbit does not exist for a null particle, however, for a massive particle such orbit exists provided its radius is larger than a minimum radius. This is in analogy with the Schwarzschild black hole as well as the YEM.

Cosmological models in [formula omitted] gravity and the dynamical system analysis

The study addresses matter-coupled modified gravity, particularly f(T,T) gravity, unveiling distinct formalism. The research further discusses stability analysis, and the dynamical system approach, exploring the dynamics of critical points to understand these models’ viability better. The dynamical system analysis of the cosmological models in f(T,T) gravity, where T and T respectively represent the torsion scalar and trace of the energy–momentum tensor has been investigated. It demonstrates how first-order autonomous systems can be treated as cosmological equations and analyzed using standard dynamical system theory techniques. Two forms of the function f(T,T) are considered (i) one with the product of trace and higher order torsion scalar and the other (ii) linear combination of linear trace and squared torsion. By employing this methodology, the research aims to uncover the actual behavior of the Universe. The findings emphasize the graphical representation of these insights, enriching our understanding of cosmological scenarios.

Revisiting [formula omitted] cosmologies

We review the status of f(R,T) cosmological models, where T is the trace of the energy momentum tensor Tμν. We start focusing on the modified Friedmann equations for the minimally coupled gravitational Lagrangian of the type f(R,T)=R+αeβT+γnTn. We show that in such a minimally coupled case there exists a useful constraining relation between the effective fractionary total matter density with an arbitrary equation of state parameter and the modified gravity parameters. With this association the modified gravity sector can be independently constrained using estimations of the gas mass fraction in galaxy clusters. Using cosmological background cosmic chronometers data and demanding the universe is old enough to accommodate the existence of Galactic globular clusters with ages of at least ∼14 Gyrs we find a narrow range of the modified gravity free parameter space in which this class of theories remains viable for the late time cosmological evolution. This preferred parameter space region accommodates the ΛCDM limit of f(R,T) models. We also work out the non-minimally coupled case in the metric-affine formalism and find that there are no viable cosmologies in the latter situation. However, when analyzing the cosmological dynamics including a radiation component, we find that this energy density interacts with the matter field and it does not scale according to the typical behavior. We conclude stating that f(R,T) gravity is not able to provide a full cosmological scenario and should be ruled out as a modified gravity alternative to the dark energy phenomena.

Chaplygin gas equation in curvature-matter coupling gravity

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density [Formula: see text] and pressure [Formula: see text], by the relationship [Formula: see text] and the curvature-matter coupling gravity as [Formula: see text], where [Formula: see text] is a positive constant, [Formula: see text] and [Formula: see text] denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form [Formula: see text], where we used two forms of [Formula: see text] and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model.

Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential.

Echoes from charged black holes influenced by quintessence

In this paper, we investigate the effective potential and echoes from dyonic black holes with quintessence. For a dyonic black hole, the quasi-topological electromagnetism provides proper matter energy–momentum tensor to curve the spacetime, and quintessence strengthens this force. We find that when the effect of quintessence becomes stronger, the black hole potential will experience a series of complex transition processes between single-peak and double-peak. This causes repeated appearance and disappearance of the black hole echoes. In particular, we find that observer will receive a sudden vanishment of high-frequency echoes when quintessence remains a relatively strong effect.