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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Lorentz invariance of the Minkowski metric

As far as I understand, one requires that in order for the scalar product between two vectors to be invariant under Lorentz transformations $x^{\mu}\rightarrow ...
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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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Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
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39 views

What is the property which flows as described by the stress energy tensor in GR?

I found the following definitions: The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of ...
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167 views

What is gravitational energy in general relativity?

In GR the curvature of spacetime "is gravity". This curvature is expressed via the Riemann tensor (or the Ricci tensor + Ricci scalar). The curvature is connected via the Einstein Field Equations with ...
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44 views

Einstein tensor as a conserved current?

As is well-known, the ``traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ...
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24 views

Stuck with physics tensile strength problem

So this was a question in my exam. I am not asking for the solution rather some help at a step. A glass spherical shell of radius $R$ has a point source of monochromatic light of wavelength ...
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56 views

Central charge in energy-momentum tensor OPE

I think that general point of view about central charge in books is considering OPE $T(z) T(w)$ for different field theories and finding that general expression for the most singular term is about to ...
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27 views

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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31 views

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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47 views

Understanding Vaidya metric and pure radiation stress-energy tensor

I am following Vaidya metric and how it is related to pure radiation from Wikipedia. But when it reaches the line where stress-energy tensor is equated to product of two four-vectors, I cannot follow ...
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How to obtain momentum four vector components from the stress energy tensor

In obtaining a momentum component as an integral of the relevant stress energy tensor component, I sometimes come across it shown as an integral of the tensor component over three space and sometimes ...
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36 views

Perfect fluid and EM tensor in rest frame

I see that we use perfect fluid which is characterized by a energy density and isotropic pressure for general forms of matter. When guessing the values of energy momentum tensor indices we can use ...
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78 views

Is $\phi^4$ theory in 4d conformally invariant at the classial level?

I used to believe the three following statements to be true (at the classical level only): From scale invariance full conformal invariance follows. Scale invariance is present if there are no ...
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150 views

Derivation of momentum in QFT - from Energy-Momentum Tensor [closed]

The conserved 4-momentum operator for the complex scalar field $\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)$ is given in terms of the mode operators in $\psi$ and $\psi^{\dagger}$ as $$P^{\nu} = \int ...
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Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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36 views

How is electromagnetic binding energy introduced in the stress-energy tensor

Take the hydrogen atom. It is easy to imagine that the gravitational pull it creates is smaller than the sum of those of the proton plus the electron, because a photon of 13.6 eV was created when the ...
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Boundary stress-energy tensor form ADS/CFT

In "Gravitational Dynamics From Entanglement "Thermodynamics"" by Lashkari/McDermott/Van Raamsdonk, the authors derive the linearised Einstein equations from ADS/CFT. At page 6 they use ...
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31 views

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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126 views

Einstein field equations and SEM tensor + Alcubierre

I wonder how I can find, using the Einstein field equations, the SEM tensor in a region of space with a function $k(x,y,x)$ that describes the curvature of space in that region at a moment (so it is ...
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63 views

What is $\mathcal{L}_M$?

Usually we derive the Einstein field equation in vacuum starting from E-H action $$S= \int{\sqrt{-g}d^4x(\frac{c^4}{16\pi G})R}.$$ But in case we wanted to get ...
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86 views

Are quantum “virtual negative-energy particles” the same as “negative energy density” in EFEs?

Question is fairly straightforward. Quantum theory describes negative energy in the form of the Casimir effect and virtual negative energy particles. In the Einstein field equations, negative energy ...
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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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227 views

What exactly is $T_{\mu\nu}$?

Continuous matter is described in special relativity by the matter tensor which is the so-called stress-energy-momentum tensor. I am finding a difficulty understanding how a tensorial tool ...
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110 views

Conformal properties of the energy-momentum tensor and Schwarzian derivative

Polchinski Vol. 1 (Sec. 2.4): I'm trying to understand the Eq. 2.4.26 where he shows how the stress tensor transforms under a conformal transformation ($z \rightarrow w$): $$(\partial w)^2 T(w) = ...
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131 views

Does increasing pressure, increase gravity?

This question might be a little misguided, given that I have never studied GR or quantum field theory, but... As I understand it, dark energy is caused by negative pressure in the gravity field. ...
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154 views

Ricci tensor as relativistic Hamiltonian

I am little bit dissapointment with action integral in General relativity. The action integral is: $$ \int Rd^{4}x=\int R_{ij}g^{ij}d^{4}x\tag{1} $$ Where $$ ...
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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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109 views

Can stress energy tensor vanish in general relativity?

When I saw the questions why matter-anti matter annihilation produces photons not gravitons, it suddenly occured to me that if the latter really happens, it means the stress energy tensor vanishes ...
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84 views

Why is gravity sensitive to absolute energies?

In QFT absolute energies play no role in the physical set-up, only relative energies (i.e. energy differences) are important. However, in general relativity this doesn't appear to be the case, I've ...
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If energy isn't globally conserved, can we extract useful “free” work?

Previously, we discussed why energy is not globally conserved under general relativity. It seems counterintuitive to me, however. Does this mean we can extract useful work from this "free" energy? ...
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83 views

Maxwell Stress Tensor at material boundaries

I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in an article ...
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61 views

Does spacetime curvature increase when an attractor's potential energy is converted to kinetic energy?

Imagine an asymptotically flat spacetime with nothing but two stars at a certain distance. They fall into each other and form one big star, so their potential energy is converted to kinetic energy. ...
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Shawyer EM Drive — Momentum Conservation Violation

I have been following the developments around the Shawyer EM drive for about 2 years now as NASA and other parties test it out in various environments. To preface, I would very much like to see the EM ...
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What component of the stress–energy tensor contains the kinetic energy of heat? [duplicate]

As I understand it, the component $T_{00}$ of the stress-energy tensor contains the energy density (which equals the mass density), $T_{0i}$ are the impulse flows (intuitively speaking, the ...
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60 views

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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79 views

What is the value of the variation stress energy tensor?

If we are living in a portion of space-time where the metric is very close to flat space and we know that the stress energy tensor is negligible at this portion of space-time is it ok to assume that ...
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1answer
85 views

Interpretation of a term in the Maxwell stress tensor

With no magnetism, the $xx$ component of the Maxwell stress tensor $T$ is $$T_{xx} = \frac{1}{2}(E_x^2 - E_y^2 - E_z^2)$$ I can see why there should be a $+E_x^2$ term, but intuitively I don't see why ...
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107 views

From Noether's theorem to canonical Energy-Momentum tensor using translations

In this text that I am reading it says that the transformation $\delta \phi(x)$ is a symmetry if the Lagrangian changes by a total derivative: $$\delta \mathcal{L}= \partial_{\mu}F^{\mu} . $$ From ...
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299 views

Energy-Momentum Tensor for Electromagnetism in Curved Space

$\newcommand{\l}{\mathcal L} \newcommand{\g}{\sqrt{-g}}$$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$I want to calculate the energy-momentum tensor in curved free space by functional ...
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Normal of a null surface and null junction conditions in general relativity

I am trying to use the null junction formalism in general relativity (as explained in eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.3763&rep=rep1&type=pdf, "Junctions and thin ...
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Can the stress energy tensor have nonzero value in a vacuum region?

In general relativity, when solving for the schwartzchild solution, we set $T=0$. 1) Is it possible for the stress energy tensor to have nonzero value in a vacuum region? 2) Is the stress $T=0$ in ...
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1answer
128 views

Why does a certain covariant derivative of the stress-energy tensor vanish due to diffeomorphism invariance?

In Polchinski's string theory volume 1, at chap 1.2, after equation 1.2.22, he says $$\nabla_{a}T^{ab}=0$$ as a consequence of diffeomorphism invariance. But I cannot derive it. My derivation is ...
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2answers
112 views

Is the stress energy tensor continuous at the interface between an object and vacuum?

The stress energy tensor has (as I understand) zero value in the region where there is no matter and non-zero value where there is matter. Suppose there is one matter object in space, now how does the ...
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1answer
111 views

Stress-energy tensor on spacetime satisfying Klein-Gordon equation

Consider the stress-energy-momentum tensor $$T_{\alpha \beta}=(\nabla_\alpha \phi )\nabla_\beta \phi -\frac{1}{2}g_{\alpha \beta}((\nabla^\nu \phi ) \nabla_{\nu} \phi +m^2 \phi^2$$ where the ...
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473 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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Non-local gravitational energy tensor

The well-known derivation of the Landau-Lifshitz gravitational energy pseudotensor, relies on several requirements: 1) that it be constructed entirely from the metric tensor 2) that it be index ...
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1answer
91 views

What is the metric of a constant electromagnetic (pure electric or pure magnetic) field?

For example, imagine a magnetic field $B_x$ directing in $\hat{x}$ direction filling all the space. What is its associated metric field? I can construct the electromagnetic stress-energy tensor for ...