The stress-energy tensor

2019 ◽  
pp. 59-65
Author(s):  
Steven Carlip
Keyword(s):  
Equations Of Motion ◽  
Scalar Fields ◽  
Gravitational Energy ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Equations ◽  
Perfect Fluids ◽  
Stress Energy ◽  
Relationship Of ◽  
The Relationship

The “source” of gravity in the Einstein field equations is the stress-energy tensor. After a discussion of why gravitational mass should be part of a rank two tensor, this chapter derives the stress-energy tensor for a variety of types of matter: point particles, perfect fluids, scalar fields, and electromagnetism. The chapter discusses the relationship of differential and integral conservation laws, and introduces the problem of gravitational energy. It concludes with a discussion of one of the most remarkable results of general relativity, the fact that equations of motion for matter do not need to be introduced separately, but follow from the field equations.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals Quaternionic electrodynamics

2020 ◽  
Vol 35 (39) ◽  
pp. 2050327
Author(s):  
Sergio Giardino
Keyword(s):  
Poynting Vector ◽  
Magnetic Monopoles ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Equations ◽  
Electrodynamic Force ◽  
Quantization Rule ◽  
Dirac Monopole ◽  
Charge Quantization ◽  
Stress Energy

We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy conservation, and the stress-energy tensor. The formalism also enabled us to generalize the Dirac monopole and the charge quantization rule.

scholarly journals A dynamical system analysis of f(R,T) gravity

2016 ◽  
Vol 13 (09) ◽  
pp. 1650108 ◽  
Author(s):  
Behrouz Mirza ◽  
Fatemeh Oboudiat
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Equation Of State ◽  
System Analysis ◽  
Equations Of Motion ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Future Singularity ◽  
First Case ◽  
Stress Energy

We investigate equations of motion and future singularities of [Formula: see text] gravity where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate [Formula: see text] gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on [Formula: see text] is studied and the consistent form of [Formula: see text] function is found using the symmetry and the conserved charge.

scholarly journals Stress Energy Quantum Tensor : Linear Approximation of the Einstein’s Equations and Equivalence with the Klein-Gordon’s equation

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
Linear Approximation ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Linearized Gravity ◽  
Stress Energy ◽  
Energy Pulse ◽  
Klein Gordon ◽  
Energy Quantum ◽  
The Relationship

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

scholarly journals Stress Energy Tensor Study in Fluid Mechanics

2019 ◽  
Author(s):  
Roman Baudrimont
Keyword(s):  
General Relativity ◽  
Fluid Mechanics ◽  
Space Time ◽  
Newtonian Fluids ◽  
Third Party ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

scholarly journals On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology

2017 ◽  
Vol 26 (13) ◽  
pp. 1750146 ◽  
Author(s):  
Marcelo M. Disconzi ◽  
Thomas W. Kephart ◽  
Robert J. Scherrer
Keyword(s):  
Equations Of Motion ◽  
Heavy Ion ◽  
Viscous Fluids ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Relativistic Fluids ◽  
First Order ◽  
Ion Collisions ◽  
Stress Energy ◽  
Barotropic Equation

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller–Israel–Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

scholarly journals Wormhole geometries in Eddington-Inspired Born–Infeld gravity

2015 ◽  
Vol 30 (35) ◽  
pp. 1550190 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak ◽  
Sergey V. Sushkov
Keyword(s):  
Exact Solution ◽  
Nonlinear Electrodynamics ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Gravitational Field Equations ◽  
Stress Energy ◽  
Modified Theory Of Gravity ◽  
Modified Theory

Eddington-inspired Born–Infeld (EiBI) gravity is a recently proposed modified theory of gravity, based on the classic work of Eddington and Born–Infeld nonlinear electrodynamics. In this paper, we consider the possibility that wormhole geometries are sustained in EiBI gravity. We present the gravitational field equations for an anisotropic stress–energy tensor and consider the generic conditions, for the auxiliary metric, at the wormhole throat. In addition to this, we obtain an exact solution for an asymptotically flat wormhole.

scholarly journals Cosmological perfect fluids in Gauss–Bonnet gravity

2019 ◽  
Vol 16 (09) ◽  
pp. 1950133 ◽  
Author(s):  
Salvatore Capozziello ◽  
Carlo Alberto Mantica ◽  
Luca Guido Molinari
Keyword(s):  
Perfect Fluid ◽  
Topological Invariant ◽  
Energy Tensor ◽  
Curvature Scalar ◽  
Stress Energy Tensor ◽  
Perfect Fluids ◽  
Stress Energy ◽  
Walker Metric ◽  
Friedmann Robertson Walker ◽  
Hubble Flow

In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.

scholarly journals The time traveler’s guide to the quantization of zero modes

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Ana Alonso-Serrano ◽  
Erickson Tjoa ◽  
Luis J. Garay ◽  
Eduardo Martín-Martínez
Keyword(s):  
Zero Mode ◽  
Massless Scalar ◽  
Energy Tensor ◽  
Massless Scalar Field ◽  
Stress Energy Tensor ◽  
Squeezed State ◽  
Time Machine ◽  
Zero Modes ◽  
Stress Energy ◽  
The Relationship

Abstract We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder.

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