Questions tagged [stress-energy-momentum-tensor]
A rank-2 tensor in relativity, which expresses the flux of energy-momentum along timelike and spacelike axes. Also known as the energy-momentum tensor. In the Einstein field equations, it is the source of gravitational fields.
1,126
questions
2
votes
0
answers
29
views
The meaning of stress tensor conservation in general relativity [duplicate]
In general relativity one has the Hilbert stress-energy tensor defined as
$$T^{\rm matter}_{ab} = -\frac{2}{\sqrt{-g}}\frac{\delta S_{\rm matter}}{\delta g^{ab}}~,$$
which is covariantly conserved i.e ...
1
vote
1
answer
39
views
Terms in the Israel Junction Conditions
I'm confused about the Israel Junction Conditions. I've seen them written several different ways so far, but here I'll use: $$K^-_{ij}-K^+_{ij}=8\pi(S_{ij}-\frac{1}{2}g_{ij}S).$$
My understanding is ...
0
votes
1
answer
38
views
Stress-energy tensor of electromagnetic wave in curved spacetime
I am trying to calculate the stress–energy tensor of an electromagnetic wave in curved spacetime, characterized by the diagonal metric
$$
g_{\mu\nu} =
\begin{pmatrix}
-g_{zz} & 0 & 0 & 0 \\...
0
votes
0
answers
23
views
Degrees of freedom in stress-energy tensor
The stress-energy tensor has 16 components, but this question is only about the 9 components $T^{ij}$ with $i,j=1,2,3$. According to Wikipedia, these components are defined as follows:
The components ...
-1
votes
1
answer
46
views
Showing that Poynting’s theorem preserved with Proca Lagrangian
The Proca Lagrangian is
$$\mathcal{L}=-\frac{1}{4\mu_0}F_{\mu\nu}F^{\mu\nu}-\frac{1}{2\mu_0\Lambda^2}A_{\mu}A^{\mu}+A_{\mu}J^{\mu}$$
Where $\Lambda=\frac{\hbar}{m_{\gamma}c^2}$.
The symmetric energy-...
1
vote
0
answers
34
views
Question on linear perturbations in cosmology
I've been studying clustering dark energy when I came across a paper named "A Short Review on clustering dark energy" by Ronaldo Batista. there are 2 equations in this paper (eq.8 and eq.9) ...
0
votes
0
answers
34
views
Pressure as momentum flux versus momentum of fluid flow
I've read in multiple sources (for example, Thorne and Blandford, Modern Classical Physics, pg 83 and Schutz, A First Course on General Relativity pg 92) that the stress components of the stress-...
1
vote
0
answers
51
views
Why symmetrization of energy-momentum tensor doesn't add additional term to Lagrangian density? [duplicate]
I am self-studying the book “James H. Luscombe, Core Principles of Special and General Relativity”. In “CHAPTER 9 : Energy-momentum of fields” of the book, it starts by introducing Noether’s theorem ...
0
votes
0
answers
54
views
How we can deduce from symmetry of $ θ^{μν} $ that total energy-momentum due to field spin is zero?
I am self-studying the book “James H. Luscombe, Core Principles of Special and General Relativity”. In “CHAPTER 9 : Energy-momentum of fields” of the book, it starts by introducing Noether’s theorem ...
0
votes
0
answers
70
views
How to mathematically describe the process of spacetime curvature?
I guess as a result of the energy-momentum tensor $T_{\mu\nu}$ coupling to a flat Minkowski metric, $\eta_{\mu\nu}$, the flat metric can become that of a curved spacetime, $g_{\mu\nu}$. How can one ...
1
vote
2
answers
98
views
Inconsistency in Virasoro expansion of stress energy
As explained in Axiom 2.3 on page 7 of https://arxiv.org/abs/1609.09523, the independence of the stress tensor $$T(y)=\sum_{n}\frac{L_n}{(y-z)^{n+2}}$$ on the choice of expansion point $z$ leads to ...
2
votes
1
answer
102
views
Is conservation of energy a local law in Quantum field theory? [closed]
From Wikipedia,
"The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for the energy-momentum tensor operator. Thus energy is conserved by the normal ...
0
votes
0
answers
28
views
Is there an intrinsic energy-momentum associated with constraining forces that don't do work?
As an example, consider a continuous charge distribution, within Maxwell's model of classical electrodynamics, that is brought from infinity onto a spherical surface at a radius $r$ from the origin. ...
0
votes
1
answer
142
views
Showing that derivative of energy-momentum tensor is equal to 0
Given,
\begin{equation}
T^{\mu\nu} = F^{\mu\lambda} F^\nu{}_{\lambda} - \frac{1}{4} \eta^{\mu\nu} F^{\lambda\sigma} F_{\lambda\sigma}.
\end{equation}
Here $(T^{\mu\nu})$ is the energy-momentum ...
0
votes
0
answers
47
views
Norm for the energy-momentum vector: what meaning/use does it have from the point of view of the energy-momentum tensor?
Many books on relativity define "mass" $M$ as the norm of the energy-momentum vector $\pmb{P} := (E, \pmb{p})$, that is, $M = \sqrt{\lvert \pmb{P}\cdot\pmb{g}\cdot\pmb{P}\rvert}$, where $\...
0
votes
2
answers
59
views
Do negative pressures in Thermodynamics lead to a negative stress energy tensor?
If we have a gas or liquid described by the van der Waals gas law with negative pressure, does that lead to a negative stress energy tensor?
Does a stretched liquid for example have a negative stress ...
0
votes
0
answers
78
views
The meaning of the stress-energy-momentum tensor
I just learned some General Relativity and have a couple of questions about the stress-energy-momentum tensor $T$.
In what follows, please let’s suppose that General Relativity and the Standard Model ...
0
votes
2
answers
44
views
How does the amount of energy bound in the gravitational field of an object relate to the energy of the object?
If I understand correctly, there is energy bound in a gravitational field, although acceleration of the body that causes the field is required to release some of that energy (in the form of ...
2
votes
0
answers
49
views
How should I calculate the commutator between the Belinfante stress tensor and the field operator?
As known, there is an ambiguity on the definition of the stress tensor (or energy-momentum tensor).
The canonical stress tensor, defined as the Noether's current corresponding to space-time ...
1
vote
1
answer
86
views
Thermal conductivity from the mass distribution of an object
Thermal conductivity is a property normally related to material. But it is also possible to relate it to objects.
Consider two objects of different shapes made by the same homogeneous material. How ...
0
votes
0
answers
51
views
Can you assume the energy-momentum tensor is symmetric if you only impose Lorentz symmetry?
The proof showing that the energy-momentum tensor is symmetric uses the fact that $\partial_\nu T^{\mu\nu}=0$ due to translation symmetry, the definition of the conserved current and that $\partial_\...
1
vote
0
answers
68
views
Confusion about the derivation of stress tensor OPE from Ward Identity
I apologize for any difficulty in expressing my review. Allow me to briefly summarize the material and then pose my question.
Review
In David Tong's string lecture note, he derives the OPE between ...
2
votes
1
answer
56
views
Canonical electromagnetic stress-energy-momentum tensor
I have canonical electromagnetic stress-energy-momentum tensor defined as:
$T_{\mu\nu}=\frac{1}{4}\eta^{\mu\nu}F_{\alpha\beta}F^{\alpha\beta}-F^{\mu\lambda}F^{\nu}_{\,\,\lambda}-F^{\mu\lambda}\...
1
vote
0
answers
45
views
Q1.1(a) Sakurai Advanced Quantum Mechanics For energy-momentum tensor [closed]
I need to prove that the energy-momentum tensor density is defined as:
\begin{equation}
\mathcal{T}_{\mu\nu}=-\frac{\partial \phi}{\partial x_\nu}\frac{\partial\mathcal{L}}{\partial(\frac{\partial \...
1
vote
1
answer
94
views
Energy-Momentum tensor in Classical Mechanics
I can compute Energy-momentum tensor in classical field theory using Noether's theorem and translation invariance of action, but I think I can't exactly calculate how to calculate same thing in ...
0
votes
1
answer
70
views
Which version of the equivalence principle affects the coordinate dependency of the Landau–Lifshitz pseudotensor?
We know that the energy-momentum of gravity can be defined by a pseudotensor called the Landau-Lifshitz pseudotensor, which is coordinate dependent. In fact, the gravitational stress–energy will ...
0
votes
1
answer
79
views
Cosmological perturbation theory and relationship to Taylor series?
In cosmological perturbation theory, it's hard to find papers that would expose the general principle to perturb physical quantities (metric, fluid pressure and density, speed...) up to the $n$th ...
3
votes
2
answers
458
views
Electromagnetic field pressure
Wikipedia gives that maxwell tensor components have minus in the electromagnetic stress energy tensor https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor. That mean the ...
0
votes
0
answers
73
views
What is the Noether stress-energy tensor?
The goal is to find the formula for the stress-energy tensor, of mass-energy field.
The Poincare group's algebra generates it with 3+3+4 generators, the first 6 or the continuous Lorentz subgroup (Let'...
2
votes
1
answer
61
views
Post-Newtonian Stress-Energy tensor
I am currently studying Michele Maggiore's book - 'Gravitational Waves: Volume 1: Theory and Experiments'. On pages 245 and 246, each order --- until the second order --- of the stress-energy tensor. ...
4
votes
1
answer
91
views
Question about proof of Weinberg-Witten theorem
In proving the Weinberg-Witten theorem, there is a step where one needs to show
\begin{align*}
\lim_{k' \to k}\langle k, \sigma | J^{\mu} |k', \sigma \rangle &= \frac{q k^{\mu}}{k^0}\frac{1}{(...
5
votes
0
answers
96
views
Derivation of the Conformal Ward Identity in Di Francesco et al
I am reading section 5.2.2. (titled The Conformal Ward Identity) from Conformal Field Theory by Di Francesco et al. The authors write
\begin{align}
\partial_\mu(\epsilon_\nu T^{\mu\nu}) &= \...
1
vote
1
answer
120
views
Stress-energy-momentum tensor and potential energy
The stress-energy-momentum tensor in General Relativity includes a mass density terms, which is related to energy via $E=mc^2$. How does potential energy figure into this, since potential energy is ...
1
vote
0
answers
51
views
How to derive WZW model’s energy-momentum tensor? The result is of course the Sugawara construction
I want to know how to derive WZW’s energy-momentum tensor. We know WZW action is
$$
S_{WZW}[g]=\frac{k}{16\pi}\int d^2x Tr(\partial g^{-1}\partial g) - \frac{ik}{24\pi}
\int_B d^3y \epsilon_{abc} Tr(h^...
1
vote
0
answers
36
views
Detailed derivation of the energy-momentum tensor from the Maxwell Lagrangian [duplicate]
I have started studying QFT, and I am currently reviewing briefly on the classical field theory. I have come across the Maxwell Lagrangian given by
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}.
$$
...
0
votes
0
answers
35
views
Local Supersymmetry and Space-time Metric
So following from Simple Supergravity (arxiv:2212.10044), on page 5, it's written that
Only the spacetime metric can couple to the energy-momentum tensor...
Can anyone explain why it must be the ...
1
vote
1
answer
127
views
Transforming stress tensor from polar to Cartesian coordinates?
Trying to understand where my calculation goes wrong. I have the stress tensor with components $T_{\rho \rho}, T_{\rho \theta}$ and $T_{\theta \theta}$. I wish to express this in Cartesian coordinates....
0
votes
1
answer
89
views
Lorentz Transformations and Angular Momentum unclear derivation
How do we get rid of $\omega^{\rho}_{\;\;\nu}$ and howt do we derive the last equation form the previous one. Here is URL for the source where I found this text page 17 (marked at bottom).
1
vote
0
answers
47
views
Stress-Energy Tensor for a Two Mass System
I just don't understand this tensor and would like to go through an example with you to somehow make sense of it.
I consider two spheres with masses $m_1$ and $m_2$, densities $\rho_1$ and $\rho_2$ ...
0
votes
0
answers
56
views
First-order formalism General relativity
I am trying to find the stress energy tensor for an ideal fluid from a first-order formalism. My matter lagrangian is $\int d^4 \sqrt{-g} [g^{\mu\nu} \partial_{\mu} \theta \partial_{\nu} \theta - V(\...
0
votes
1
answer
68
views
Stress-energy tensor spin-1 coupling
Would it be possible for the stress-energy tensor ($T_{\mu\nu}$) to couple to a spin-1 anti-symmetric rank-2 field (like the electromagnetic field strength tensor $F_{\mu\nu}$)? If so, what would be ...
0
votes
0
answers
87
views
Trace of stress-energy tensor for a scalar field
I'm trying to reproduce a calculation done in Birrell & Davies' book Quantum Fields in Curved Space (page 191). Given Klein-Gordon's equation $$(\Box + m^2 + R\xi)\phi = 0$$ and
$$T_{\mu \nu} = (1 ...
1
vote
1
answer
73
views
Proof of energy-momentum tensor is zero in Polyakov action
The polyakov action is defined as
\begin{equation}
S=-\frac{T}{2}\int d\sigma d\tau \sqrt{-h}h^{\alpha \beta} \partial_{\alpha}X^{\mu}\partial_{\beta}X^{\nu}\eta_{\mu \nu}
\end{equation}
by varing ...
0
votes
0
answers
54
views
About Noether currents for conformal symmetries
I´m reading "Conformal algebra on Fock space and conjugate pairs of operators" of
Klaus Sibold and Eden Burkhard, there the authors write all Noether currents in terms of the energy momentum ...
0
votes
0
answers
38
views
Trace of stress tensor in 2D average null energy condition
I was looking through Zamolodchikov's derivation of the $c$-theorem and stumbled across an equation which says the following -
$$\Theta = T^\mu_\mu = 4T_{z\bar{z}}.$$
As far as I understand, for two ...
2
votes
1
answer
161
views
Problem 3.3 b) of Schwartz's Quantum Field Theory
In problem 3.3 b) of Schwartz's Quantum field theory you are asked to prove that $ Q = \int T_{00} d^3x $ is invariant under changing the Lagrangian $ \mathcal{L} \rightarrow \mathcal{L} + \partial_\...
0
votes
1
answer
64
views
The Electromagnetic Energy and Momentum Conservation in curved space-time
Can someone please show me the formalisms of the energy and the momentum conservation in the curved space-time for electromagnetic?
I know it's going to be two equations.
but I couldn't find them ...
22
votes
4
answers
3k
views
Does the gravitational field have a gravitational field?
I am currently reading electrodynamics from Feynman. When talking about the energy of the electromagnetic fields, he says that the location of the field energy could be known at least theoretically ...
1
vote
1
answer
397
views
Trying to understand how to apply Maxwell stress tensor to calculate forces
I'm struggling to understand how to use Maxwell's stress tensor to compute electromagnetic forces acting on surfaces. I'll take problem 8.7 from Griffths Introduction to Electrodynamics as an example.
...
1
vote
1
answer
159
views
Stress-energy tensor for a massive particle in the electromagnetic field
I want to write down the expression for the stress-energy tensor for a massive particle in the electromagnetic field such that it can be split into two parts for the massive term and the field term, ...