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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.

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Using Maxwell Stress Tensor to get force between two current-carrying wires

I’m trying to find the force per unit length between two parallel wires carrying the same current in the same direction and a distance of 2a apart. I need to use the Maxwell stress tensor and am ...
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When and how was the need for symmetry in the stress-energy tensor first realized

This question is somewhat historic. Let $\Theta_{\mu\nu}$ denote the canonical stress-energy tensor of some matter field $\psi$ in special relativity. It is often stated that the reason why we want ...
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Derive conservation laws for the energy momentum tensor, $T μν$ in coordinates $(τ,x,y,η)$

How can i derive this relation? i need simulation Transverse momentum spectra of π+ and K+ , but i do not know what discretized this tensor coupled partial differential equations`]1
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Momentum in capacitor field; How can an EM field have zero momentum density but non-zero momentum flux?

Consider the case of a simple, stationary parallel plate capacitor oriented with its plates lying in the x-y plane. The E-field is simply given by: $$\vec{E} = \frac{Q}{\epsilon_0A}\hat{z} $$ with ...
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Sign mistake in the energy momentum tensor of the Klein-Gordon Equation

Recently I understood that the energy momentum tensor can be calculated by: \begin{equation} T_{\mu \nu}=\frac{2}{\sqrt{-g}}\frac{\delta S_m}{\delta g^{\mu \nu}}.\tag{1} \end{equation} So consider ...
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What kind of average could give a Lorentz invariant energy-momentum tensor?

The electromagnetic (EM) radiation energy-momentum tensor is of the following shape, in the case of incoherent superposition of EM plane waves (I'm using $c = 1$ to simplify things, and metric ...
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Confusion about conservation of angular momentum tensor in classical field theory?

In my lectures, we considered the conserved stress energy tensor $T^{\mu \nu}$ and noted that we could always add a conserved tensor to it such that $T^{\mu \nu}$ is symmetric. As a consequence, a ...
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Demonstration of magnetic field lines “tension” and “pressure” using the Maxwell stress tensor

I would like to show that the magnetic fields lines are under "tension" along the lines and exert "pressure" perpendicularly to the lines, using the Maxwell tensor only. I have a sign ambiguity. In ...
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How do compute an energy momentum tensor, given some equations of motion

This problem can be found in a paper called "Gravitational Radiation From Point Masses In A Keplerian Orbit", but I do not have access to this, so cannot see how to do it. I have been given a ...
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42 views

Angular momentum of a circualr polarized EM wave

In an exercise, I am being asked to compute the angular momentum of a circularly polarized wave. The wave is defined by the four potential: $$\Phi^\mu(x^\nu) = \text{Re} \left\{ \varepsilon^\mu e^{...
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Hanging two charged sphere by a light string

NB: This is not a homework question. I am not searching for any solution of a math problem. I found something incorrect to do always in the nature of two charged pith balls hanging from a light ...
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Constraints in general relativity

In this review on inflation, on Pg. 135, Baumann talks about the energy and the momentum constraints for gravity. Are these equations the $G_{00} = T_{00}$ and $G_{0i} = T_{0i}$ components of the ...
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Proof of the existence of the energy-momentum tensor [duplicate]

I have a problem providing or finding a general proof for this statement i found in Mussardo's statistical field theory book, section $10.3.2$: Due to the locality of the theory there exists a local ...
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Is it possible to define an energy momentum tensor for classical point particles from a QFT?

I have a question about the semi-classical limit of a QFT that so far I have never been able to solve. Let's start with a second quantized Klein-Gordon field with Lagrangian $$\mathcal{L}(\phi)=\frac{...
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Why are the diagonals of the pressure tensor non-negative?

I understand that the pressure tensor is simply the momentum flux which makes sense to me (pressure is force per unit area which is momentum change per unit time per unit area). From this, a simple ...
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Stress Tensor decomposition into Compression & Tensile forces

this might be a little more of an engineering question that physics but physics is my background so asking here... I'm working on a project that does a finite element simulation of a mesh. I can ...
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Absorbing the Cosmological “Constant” in the standard Energy-Stress Tensor

Recently I found some publications on Cosmologies with variable cosmological constant. The Bianchi Identity then implies that the divergence of the modified Energy Stress: Tensor $$\hat{T}_{ab}=T_{ab}...
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Double divergence of stress tensor for migration flux

I am looking to calculate migration as a function of time using equation in Image 1. SigmaP is the total particle stress tensor in the cylindrical coordinates (r, theta, z). I am only interested in ...
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Einstein GR and metric signature

Let us take the einstein Equation $R_{\mu\nu} -\frac{1}{2}g_{\mu\nu}R = T_{\mu\nu}$. I'm just ignoring all the constants. For a perfect fluid, $$T_{\mu\nu} = (\rho + P)u_{\mu}u_{\nu} - Pg_{\mu\nu}.$$ ...
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What does it mean if the Lagrangian density has explicit spatial dependence?

First off, I have seen this post here which asks seems to ask my question, but it is not properly answered. If the Lagrangian has explicit time dependence, then the total energy, and Hamiltonian, is ...
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How much of Maxwell's equations is recoverable from the zero divergence of the stress-energy tensor?

As a motivating example, consider the static electromagnetic field defined by $\textbf{E}=(\text{const})x\hat{\textbf{y}}$, $\textbf{B}=0$. The stress-energy tensor for this field is $T=\operatorname{...
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Conservation of improved energy momentum tensor of a real massless scalar field

So I'm supposed to find that the improved energy momentum tensor of the scalar field $\phi$ satisfying the evolution equation $\Box \phi = 0$ is conserved. The improved energy momentum tensor is: $T^{...
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Noether charges of spacetime translation in KG field

When applying a spacetime translation $x^\mu\rightarrow x^\mu+a^\mu$ the KG lagrangian density changes by - $$\mathcal{L} \rightarrow \mathcal{L} + a^\nu \partial_\mu \delta^\mu_{\;\nu} \mathcal{L}$$...
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What is the geometric interpretation of the Einstein tensor $R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R$

The Riemann curvature tensor $R_{\mu \nu \rho \sigma}$ has the geometric interpretation of giving how much parallel transport fails to close around tiny loops. The Ricci tensor $R_{\mu \nu}$ the ...
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Stress-Energy Tensor of Electromagnetic Field with sources

I can find a lot of references which treat the derivation of Maxwell equations and the associated Energy-Stress Tensor from the action principle. But I cannot find any information on the Energy-Stress ...
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Divergenceless of energy momentum tensor for any metric $g_{\mu\nu}$

As suggested by @my2cts, from this post, I want to know if the divergenceless of energy-momentum energy tensor is valid for any metric $\eta_{\mu\nu}$ (i.e for example with $\eta_{\mu\nu}=g_{\mu\nu}$)?...
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Sign problem in electromagnetic stress energy tensor

I'm having a silly problem in calculating the electromagnetic stress energy tensor: the Lagrangian is $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$ and the stress energy tensor reads $$ T^{\mu\...
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Get relation from definition of stress-energy tensor and the conservation of energy

Starting from the following definition of stress-energy tensor for a perfect fluid in special relativity : $${\displaystyle T^{\mu \nu }=\left(\rho+{\frac {p}{c^{2}}}\right)\,v^{\mu }v^{\nu }-p\,\eta ...
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building expression for momentum from stress energy tensor

Let's say I have a stress-energy tensor with the the following non-zero components: the diagonal components $T^{00}, T^{11}, T^{22}, T^{33} $ and $T^{10}=T{01}$. I know that the energy density is just ...
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176 views

Schwarzian derivative from conformal factor

Suppose I have a 2D Lorentzian conformally flat metric $$ ds^2 = -\Omega(u, v) du dv.$$ I consider a conformal field theory whose stress-energy tensor $T_{ab}$ is known on the flat metric $$ds^2 = -...
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Derivation of the energy-momentum tensor from matter Lagrangian

We know that the energy momentum tensor for a perfect fluid is given by $$ T_{\mu\nu} = \left(\rho+{p\over c^2}\right) v_\mu v_\nu + p g_{\mu\nu}. $$ How can we derive it from a Lagrangian? Which ...
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non-zero divergence of stress energy tensor

are there spacetime metrics where $\nabla_{\nu}T^{\mu\nu} \ne 0$ ? if the divergence of the energy momentum tensor is non-zero, what does that tell us about the spacetime aside from the fact that ...
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Transformation of the Stress-Energy tensor [closed]

My question is related to this one. However in my case, the Lagrangian can depend on higher order derivatives (so the second point made doesn't hold). Can someone help me with it?
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What exactly is a Stress-Energy tensor?

I am very new to physics and have recently come across the term stress-energy tensor. I am completely clueless as to what this is, and the Wikipedia page seems to confuse me even more. Can someone ...
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Gravitational waves energy source in linearized theory

By linearizing the metric in the following way (approach in most textbooks): $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\text{ with } |h_{\mu\nu}|\ll 1$ and choosing the transverse-traceless gauge a wave ...
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Energy-momentum tensor non-minimal scalar field

If we consider a non-minimal coupling term between gravity and scalar field for inflation, we can have some modifications for density and pressure of scalar field. I have some problems to obtain the ...
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Energy Momentum Tensor and Conserved Current

I have $$j_{\epsilon} = T_{\mu\nu}\epsilon^{\nu}.$$ I need to show $$\nabla_{\mu}j^{\mu} = 0,$$ which I am told is possible via taking into account the Killing equation $$\partial_{\mu}\...
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Stress Energy Tensor in language of differential forms

The motivation for this is that quantities like the electric current $J$ in maxwell's equations of motion can be expressed as a differential 3-form, so that the continuity equation can be written just ...
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Does an electromagnetic field affect neutral particles via the metric because of the EM stress-energy tensor?

I'm just starting to learn general relativity (GR), and I'm a beginner, but I came out with this situation which is unclear to me: The trajectory of a charged particle in GR is given from the equation:...
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General Relativity: Metric tensor in terms of the stress-energy tensor?

The stress-energy tensor can be expressed in terms of the metric tensor, and its first two derivatives. An example can be found here: https://en.wikipedia.org/wiki/Einstein_tensor However, is the ...
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How can energy density (of the same sign) have opposite effects on the curvature of the universe?

Actually I have been inspired by the post Why does dark energy produce positive space-time curvature? to ask the following question. In difference to the just cited post I will take the pressure out ...
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In what sense is the stress-energy tensor the derivative with respect to the metric?

In Di Francesco et al (the big yellow book), section 2.5.2, it is suggested that the (symmetrized) stress energy tensor can be interpreted as the functional derivative of the action with respect to he ...
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Does Higgs field exert pressure which contributes to the stress-energy tensor causing gravity?

First of all, I have never studied quantum field theory. Since Higgs field is a scalar field, does Higgs field also exert positive/negative pressure which contributes to the stress-energy tensor ...
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Stress energy tensor of perfect fluid in general frame [closed]

Good day to everyone. I have a problem with the stress energy tensor of a perfect fluid. In the frame of reference of the fluid the stress energy tensor is $T^{\mu \nu} = \left( \begin{array}{cccc} ...
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Decomposition of the symmetric part of a tensor

The rate of strain tensor is given as $$e_{ij} = \frac{1}{2}\Big[\frac{\partial v_i}{\partial x_j}+ \frac{\partial v_j}{\partial x_i}\Big]$$ where $v_i$ is the $i$th component of the velocity field ...
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Landau and Lifshitz argument for symmetry of stress tensor

In Landau and Lifshitz's book on the theory of elasticity (vol 7, theoretical physics series), specifically section 2 of the first chapter, the authors present an argument for justifying the symmetry ...
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Can the fact that dark energy increases with volume be explained by classical thermodynamics?

Considering adiabatic process in classical thermodynamics, a normal substance with (positive) pressure must do work on its environment in order for the volume to increase by $ dV $(like pushing the ...
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Why is $K \cdot T$ a conserved vector?

I am following along Chapter 2 of Takagi's Vacuum Noise and Stress Induced by Uniform Acceleration. For a free real scalar field $\phi$ the stress-energy tensor is: $$ T_{\mu\nu} = ( \partial_{\mu} \...
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108 views

Integration by parts in general relativity - boundary terms and Stokes theorem

I am trying to prove that the stress-energy-momentum Hilbert tensor satisfies a conservation law if one assumes diffeomorphism invariance of general relativity. I have taken the definition of the SEM ...
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Determining the stress-energy tensor from the equations of motion

I have a question on finding the stress-energy tensor from the equations of motion in general relativity. Given the Einstein-Hilbert action+matter Lagrangian, it is straightforward to then determine ...