# 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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### Proving the tensor virial theorem

In Schutz's Relativity Chapter 4, problem 23b) states: Use the identity $T^{\mu\nu} _{~~~~~,\nu} = 0$ to prove the following results for a bounded system (i.e. a system for which $T^{\mu\nu} = 0$ ...
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### Are the concepts of kinetic energy, potential energy etc not valid in general relativity?

In Newtonian physics, we come across different forms of energy, such as kinetic energy, potential energy etc. But in general relativity, we find only the total energy that is obtained from the energy-...
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### 1st order approximation to energy-momentum tensor of gravitational field

I was studying linearized gravity and this approximation was given without any derivation. It might be clear for others but I'm quite new on GR and I'm not sure how to get this first order ...
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### The conditions under which a stress tensor $T^{\mu\nu}$ exists

I used to believe that the existence of the stress tensor in a QFT has to do with translation invariance: "If a theory is translation invariant, then one can construct a conserved $T^{\mu\nu}$ by ...
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### Covariant Derivative and energy momentum tensor

In this reference https://arxiv.org/abs/hep-th/0307199 pag.60, it is said that it is possible to find an infinitesimal spacetime diffeomorphism (a vector field) $X_{\nu}$ independently to its ...
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### Einstein field equation specific solution

Do Einstein's field equations admit a solution such that spacetime was empty in the past of a hypersurface of constant time say $t =0$, but in the future there exists a non-vanishing energy momentum-...
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### Equation in Field Quantization Greiner

Hello, I dont understand the red part. Shouldn't it have minus instead? Sorry for lack of formatting, I only have a phone.
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### Spin part of the angular momentum from the Lagrangian

For fermions of spin $1/2$ the angular momentum has following form: $$\mathcal{J}_z = \int d^{3}x \ \psi^{\dagger} (x) \left[i(- x \partial_y + y \partial_x) + i\sigma^{xy} \right] \psi(x)$$ Here ...
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### Continuity equation for the stress-energy tensor in the FLRW metric

I'm trying to compute the continuity equation for the stress-energy tensor $\nabla^\mu T_{\mu\nu}$ in the FLRW metric $$ds^2=-dt^2+a^2(t)ds^2_3$$ where $ds^2_3=g^3_{ij}dx^idx^j$ is the metric for the ...
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### Why are shear-stress and momentum-flux the same in the GR?

I am investigeting the meaning of the components of the Stress-Energy tensor: My source also states, that this matrix is always symmetric in the General Relativity. That looks obvious on the image - ...
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### Are these conservation laws always true?

Imagine a system of particles with the internal force on $i^{th}$ particle due to $j^{th}$ particle being given as $f_{ij}$ From the derivation of law of conservation of momentum and law conservation ...
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### How to get Levi-Cevita symbol in the derivation for angular momentum using Noether's theorem? (David Tong Ex Sheet 1 Q6)

Working through David Tong's sheet here https://www.damtp.cam.ac.uk/user/tong/qft/oh1.pdf and can't follow how to get the Levi-Cevita symbol out the front? Its equation 15. I was looking at trying to ...
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### Stress tensor force equilibrium in Feynman lecture book

I was reading about tensors and especially stress tensors in Feynman lectures on physics Which is on the webvsite enter link description here While reading the “31-6. The tensor of stress”, I was a ...
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### How does one add matter coupling terms to the linearized Lagrangian for General Relativity?

In Spacetime and Geometry, Dr. Carroll provides a Lagrangian for Einstein's equations in vacuum assuming that the metric can be written in the form $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$. The ...
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### Why is there an extra term in definition of Noether current for spacetime translations?

I am reading Schwartz's Quantum Field Theory textbook. In chapter 3, Schwartz first defines the conserved current for a symmetry $\phi \rightarrow \phi + \delta \phi$ that depends on a parameter \$\...