# Tagged Questions

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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### Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
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### “Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
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### Applying Weak Energy Condition for a specific energy-momentum tensor

So, I have a particular energy-momentum tensor, for a specific line element, and I want to check if this obeys the weak energy condition ($T_{ \mu \nu} U^\mu U^\nu \geq 0$ where $U^\mu$ and $U^\nu$ ...
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### Stress Energy Tensor of EM Field

Stress energy tensor for electromagnetic field is given by $$T^{\mu\nu}=\frac1{4\pi}(F^{\mu\alpha}F^{\nu}{}_\alpha-\frac14 g^{\mu\nu} F_{\alpha\beta}F^{\alpha\beta}).$$ My textbook (unpublished ...
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### How to prove the energy of gravity in general relativity is non-local?

Every textbook in general relativity containing the energy of gravity all says that the energy of gravity is non-local and every energy-momemtum density received is pseudo-tensor, but "having not ...
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### Scale invariance and stress energy tensor

I have seen in a paper [1] that in a quantum field theory scale invariance takes place provided the stress energy tensor is traceless. How this is true? References: "INFINITE CONFORMAL SYMMETRY IN ...
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### Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields $$S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} ,$$ ...
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### Imaginary part of the stress-energy tensor

I just encountered in an article of D. G. Boulware ("Quantum Field Theory in Schwarzschild and Rindler Spaces", Phys. Rev. D 11, 1404, 1975, in the last paragraph of the Introduction) the statement ...
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### Can nonconserved energy in GR be thought of as going into gravitational field energy?

One of the most striking features of GR is that energy is not conserved. Carroll's GR text has an interesting statement about this: Clearly, in an expanding universe... the background is changing ...
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### OPE coefficents and commutation relations, and OPE with stress tensor

Basic question about conformal field theory: In a conformal field theory in $d\geq 3$ dimensions, what is the relation between commutation relations and OPE coefficients? In particular, because ...
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### Second derivative of the stress-energy tensor

Which physical meaning can have if the second derivative of stress-energy tensor is zero? In General Relativity or elsewhere.
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### Warping function for torsion of non-circular prism

I have a few questions regarding the case of torsion of a prism, as encountered in continuum mechanics. Specifically, a prism (which can be a cylinder, a rectangular prism, elliptical prism, etc.) has ...
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### What is the explicit form of $\tau^{\alpha\beta}$ in the linearized Einstein field equations $\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta}$?

If we let $h^{\alpha\beta}=\eta^{\alpha\beta}-g^{\alpha\beta}\sqrt{|det(g)|}$ then, according to wikipedia, the Einstein Field Equations become $$\Box h^{\alpha\beta}=-16\pi\tau^{\alpha\beta},$$ where ...
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### Photon Gas Stress-Energy Tensor

In standard texts it is typically discussed how one can obtain the stress energy tensor of a perfect fluid, in both coordinate-dependent and coordinate independent forms: \mathbf{T}=(\...
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### How is momentum conserved in this electromagnetic scattering?

It is well known that verifying momentum and energy conservation in the presence of electromagnetic fields requires care as the fields themselves carry energy and momentum (see Griffiths chapter 8 for ...
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### Breakdown of correspondence principle: null dust case

In both quantum and general relativity theories we are used to provide results in the "limited" conditions to demonstrate a correspondence between new and old formalism. For instance deflection of ...
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### Stress-Energy Tensor of Riemann's Curvature Field

Einstein, in "The Foundation of the General Theory of Relativity," as well as most modern lecturers in the subject, use a pseudo-tensor for the stress-energy of the gravitational field. By ...
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### Solving the Stress-energy-momentum tensor with metric

Let's say I want to find an expression for $T_{00}$ in Einstein field equations given a particular metric. I need to find first $g_{00}$, which is not complicated to find, and $R_{00}$ which is ...
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### Hilbert Stress Energy Tensor for fermions + EM field and Yang-Mills theory (fermions + gluons)

@Qmechanic or anyone else who knows the reference. I am trying to find a references to the work(s) where thorough derivation of Hilbert Stress Energy Tensor for fermions + EM fields and Yang-Mills ...
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### Show that $M^{\mu\nu}$ describes the angular momentum of the system

Define $M^{\mu\nu}$ = $\int d^3x(x^\mu T^{0 \nu}-x^{\nu}T^{0 \mu})$ describes the angular momentum of the system. I don't want you to solve it but I'm not really sure what kind of criterion it ...
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### Prove that $T_{00}$, $T_{10}$, $T_{01}$, and $T_{11}$ are all $L/(4\pi x^2)$ at $(ct, x, 0, 0)$ for star of constant luminosity $L$

We have a star of constant luminosity $L$. We want to prove that the components $T_{00}$, $T_{10}$, $T_{01}$ and $T_{11}$ are all the same for the event $(ct,x,0,0)$ and they are all $L/(4\pi x^2)$. ...
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### Symmetry of the Gravitational Stress Energy pseudo tensor

Recently, I have been reading on the Gravitational Stress-Energy pseudo tensor. It says in Wikipedia that one of the conditions for a suitable GSE pseudo tensor is that it has to be symmetric about ...