Derivation of the Symmetric Stress-Energy-Momentum Tensor in Exterior Algebra

We present a derivation of a manifestly symmetric form of the stress-energy-momentum using the mathematical tools of exterior algebra and exterior calculus, bypassing the standard symmetrizations of the canonical tensor. In a generalized flat space-time with arbitrary time and space dimensions, the tensor is found by evaluating the invariance of the action to infinitesimal space-time translations, using Lagrangian densities that are linear combinations of dot products of multivector fields. An interesting coordinate-free expression is provided for the divergence of the tensor, in terms of the interior and exterior derivatives of the multivector fields that form the Lagrangian density. A generalized Leibniz rule, applied to the variation of action, allows to obtain a conservation law for the derived stress-energy-momentum tensor. We finally show an application to the generalized theory of electromagnetism.

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

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.

Quasilocal conservation laws in cosmology: A first look

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.

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

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.

Cosmology in modified f(R,T)-gravity theory in a variant Λ(T) scenario-revisited

Three new cosmological models of the present Universe are obtained with [Formula: see text] modified theory of gravity proposed by Harko et al. [Phys. Rev. D 84 (2011) 024020, arXiv:1104.2669 [gr-qc]] in a general class of Bianchi space-time. In this paper, we have generalized the modified [Formula: see text] field equations with [Formula: see text]-gravity, where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the stress–energy–momentum tensor, respectively. To find the deterministic solutions we have considered the linearly varying deceleration parameter [Formula: see text] proposed by Akarsu and Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys. 51 (2011) 612]. We have made the analyses of the variation of pressure, energy density and cosmological term with cosmic time. It is observed that our derived models are unstable in early time whereas they are stable at late and future time (i.e. at present epoch). The physical and geometric properties of all three models are studied in detail.

Higher-derivative f(R,□R,T) theories of gravity

In literature, there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress–energy–momentum tensor [Formula: see text]. This type of modified gravity is denoted [Formula: see text] in which [Formula: see text] is Ricci scalar [Formula: see text]. We extend manifestly this model to include the higher derivative term [Formula: see text]. We derived equations of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter (dS) solution is unstable for a generic type of [Formula: see text] model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.

CONTROLLABILITY OF NONHOLONOMIC BLACK HOLES SYSTEMS

This paper studies the sub-Lorentz–Vrănceanu geometry and the optimal control of nonholonomic black hole systems. This is strongly connected to the possibility of describing a nonholonomic black hole system as kernel of a Gibbs–Pfaff form or by the span of four appropriate vector fields. Joining techniques from sub-Riemannian geometry, optimal control and thermodynamics, we bring into attention new models of black holes systems. These are reflected by the original results: a Lorentz–Vrănceanu geometry on the total space, a new sub-Lorentz–Vrănceanu geometry, a new stress–energy–momentum tensor, original solutions to Einstein field equations, and the controllability of nonholonomic black holes systems by uni-temporal or bi-temporal controls.

PECULIAR ANISOTROPIC STATIONARY SPHERICALLY SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS

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.

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

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.