The stress-energy-momentum tensor of the Gauss map in the extended nonlinear σ-model

1983 ◽  
Vol 74 (2) ◽  
pp. 159-166 ◽  
Author(s):  
B. Nielsen
Keyword(s):  
Energy Momentum Tensor ◽  
Gauss Map ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Stress Energy Momentum Tensor

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 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.

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

2021 ◽  
Vol 2090 (1) ◽  
pp. 012050
Author(s):  
Ivano Colombaro ◽  
Josep Font-Segura ◽  
Alfonso Martinez
Keyword(s):  
Energy Momentum Tensor ◽  
Flat Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Exterior Algebra ◽  
Leibniz Rule ◽  
Exterior Calculus ◽  
Stress Energy ◽  
Lagrangian Densities ◽  
Stress Energy Momentum Tensor

Abstract 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.

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.

scholarly journals Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective

Fluids ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 1 ◽  
Author(s):  
Christian Cardall
Keyword(s):  
Fluid Dynamics ◽  
Particle Number ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Balance Equations ◽  
Tensor Decompositions ◽  
Relativistic Fluid ◽  
Stress Energy ◽  
General Relativistic ◽  
Classical Particles

A kinetic theory of classical particles serves as a unified basis for developing a geometric 3 + 1 spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and inertia rather than momentum and energy; and, consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-inertia or inertia-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum (1, 1) tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully 3 + 1 form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic fluid dynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange–Euler and general relativistic formulations.

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