scholarly journals PECULIAR ANISOTROPIC STATIONARY SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS

2012 ◽  
Vol 27 (09) ◽  
pp. 1250044 ◽  
Author(s):  
EMANUEL GALLO ◽  
OSVALDO M. MORESCHI
Keyword(s):  
Dark Matter ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Stress Energy ◽  
Stress Energy Momentum Tensor

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a nonvanishing spacelike components of the stress–energy–momentum tensor. In spite of its strange nature, this solution has nontrivial descriptions of gravitational effects. We show that the main aspects found in the dark matter phenomena can be satisfactorily described by this geometry. We comment on the relevance it could have to consider nonvanishing spacelike components of the stress–energy–momentum tensor ascribed to dark matter.

Study of gravitational decoupled anisotropic solution

2019 ◽  
Vol 28 (16) ◽  
pp. 2040004
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Anisotropic Model ◽  
Field Equations ◽  
Anisotropic Solution ◽  
Spherically Symmetric Solution ◽  
Gravitational Source ◽  
The Stability

This paper formulates the exact static anisotropic spherically symmetric solution of the field equations through gravitational decoupling. To accomplish this work, we add a new gravitational source in the energy–momentum tensor of a perfect fluid. The corresponding field equations, hydrostatic equilibrium equation as well as matching conditions are evaluated. We obtain the anisotropic model by extending the known Durgapal and Gehlot isotropic solution and examined the physical viability as well as the stability of the developed model. It is found that the system exhibits viable behavior for all fluid variables as well as energy conditions and the stability criterion is fulfilled.

Comparative study of transit FLRW and axially symmetric cosmological structures with domain walls in f(R, T)-gravity

2020 ◽  
Author(s):  
Umesh Kumar Sharma ◽  
Ambuj Kumar Mishra ◽  
Anirudh Pradhan
Keyword(s):  
Domain Walls ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Axially Symmetric ◽  
Field Equations ◽  
Stress Energy ◽  
Thick Domain Walls ◽  
Theory Of Gravitation ◽  
The Universe ◽  
Stress Energy Momentum Tensor

In the present article, we study the physical and geometric scene of the inflection of the Friedmann- Lemaitre-Robertson-Walker (FLRW) and an axially symmetric (AS) perfect fluid Universe with thick domain walls in f(R, T) theory of gravitation [Harko et al., Phys. Rev. D {84} (2011) 024020], where R and T represent Ricci scalar and trace of the stress energy-momentum tensor respectively in the scenario of decelerating-accelerating transition phases. To ascertain the exact solution of the corresponding field equations, we use the concept of a time-subordinate deceleration parameter (DP) which brings forth the scale factor a(t) = sinh^{\frac{1}{n}}(\alpha t), where n and \alpha are positive parameters. For n\in (0.27, 1], a class of accelerating phase is ensured while for n > 1, the Universe attains a phase transition from positive (decelerating) to negative (accelerating) which is uniform with recent observations. The models have been tested for physically acceptable by using stability. More or less physical and geometric behavior of the models are also devoted.

scholarly journals THE LOCALLY COVARIANT DIRAC FIELD

2010 ◽  
Vol 22 (04) ◽  
pp. 381-430 ◽  
Author(s):  
KO SANDERS
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Covariant Quantum ◽  
Dimensional Spacetime ◽  
Stress Energy ◽  
Hadamard States ◽  
Stress Energy Momentum Tensor

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

scholarly journals Positive Energy Driven CTCs In ADM 3+1 Space – Time of Unprotected Chronology

2021 ◽  
Author(s):  
Deep Bhattacharjee
Keyword(s):  
Energy Density ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Exotic Matter ◽  
Positive Energy ◽  
Spacelike Hypersurfaces ◽  
Stress Energy ◽  
Maxwell Fields ◽  
Stress Energy Momentum Tensor

Chronology unprotected mechanisms are considered with a very low gravitational polarization to make the wormhole traversal with positive energy density everywhere. No need of exotic matter has been considered with the assumption of the Einstein-Dirac-Maxwell Fields, encountering above the non-zero stress-energy-momentum tensor through spacelike hypersurfaces by a hyperbolic coordinate shift.

scholarly journals Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

scholarly journals ON THE NATURAL GAUGE FIELDS OF MANIFOLDS

2000 ◽  
Vol 15 (32) ◽  
pp. 1991-2005 ◽  
Author(s):  
A. B. PESTOV ◽  
BIJAN SAHA
Keyword(s):  
Displacement Field ◽  
Energy Momentum Tensor ◽  
Linear Connection ◽  
Momentum Tensor ◽  
Gauge Fields ◽  
Spherically Symmetric ◽  
Time Inversion ◽  
Field Equations ◽  
Gauge Invariant ◽  
Minkowski Space Time

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.

scholarly journals The electrodynamics of inhomogeneous rotating media and the Abraham and Minkowski tensors. I. General theory

2010 ◽  
Vol 467 (2125) ◽  
pp. 59-78 ◽  
Author(s):  
Shin-itiro Goto ◽  
Robin W. Tucker ◽  
Timothy J. Walton
Keyword(s):  
Electromagnetic Fields ◽  
Energy Momentum Tensor ◽  
Killing Vector ◽  
Momentum Tensor ◽  
Force Density ◽  
Primary Role ◽  
Inertial Property ◽  
Acceleration Field ◽  
Stress Energy ◽  
Stress Energy Momentum Tensor

This is paper I of a series of two papers, offering a self-contained analysis of the role of electromagnetic stress–energy–momentum tensors in the classical description of continuous polarizable perfectly insulating media. While acknowledging the primary role played by the total stress–energy–momentum tensor on spacetime we argue that it is meaningful and useful in the context of covariant constitutive theory to assign preferred status to particular parts of this total tensor, when defined with respect to a particular splitting. The relevance of tensors, associated with the electromagnetic fields that appear in Maxwell’s equations for polarizable media, to the forces and torques that they induce has been a matter of some debate since Minkowski, Einstein and Laub, and Abraham considered these issues over a century ago. The notion of a force density that arises from the divergence of these tensors is strictly defined relative to some inertial property of the medium. Consistency with the laws of Newtonian continuum mechanics demands that the total force density on any element of a medium be proportional to the local linear acceleration field of that element in an inertial frame and must also arise as part of the divergence of the total stress–energy–momentum tensor. The fact that, unlike the tensor proposed by Minkowski, the divergence of the Abraham tensor depends explicitly on the local acceleration field of the medium as well as the electromagnetic field sets it apart from many other terms in the total stress–energy–momentum tensor for a medium. In this paper, we explore how electromagnetic forces or torques on moving media can be defined covariantly in terms of a particular 3-form on those spacetimes that exhibit particular Killing symmetries. It is shown how the drive-forms associated with translational Killing vector fields lead to explicit expressions for the electromagnetic force densities in stationary media subject to the Minkowski constitutive relations and these are compared with other models involving polarizable media in electromagnetic fields that have been considered in the recent literature.

scholarly journals General approach to the Lagrangian ambiguity in f(R, T) gravity

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
G. A. Carvalho ◽  
F. Rocha ◽  
H. O. Oliveira ◽  
R. V. Lobato
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Unknown Variable ◽  
Stress Energy ◽  
The Standard Model ◽  
Theories Of Gravity ◽  
Matter Fields

AbstractThe f(R, T) gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, R, and the trace of the stress–energy tensor, T; its field equations also depend on matter Lagrangian, $$\mathscr {L}_{m}$$ L m . In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the $$\mathscr {L}_{m}$$ L m dependence from f(R, T) gravity field equations by generalizing the approach of Moraes in Ref. [1]. We also propose a general approach where we argue that the trace of the energy–momentum tensor must be considered an “unknown” variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy–momentum tensor of the f(R, T) gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

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