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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Does non-mass-energy generate a gravitational field?

At a very basic level I know that gravity isn't generated by mass but rather the stress-energy tensor and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ ...
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The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
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Symmetry of the stress tensor

When presenting the stress tensor (say in a non-relativistic context), it is shown to be a tensor in the sense that it is a linear vector transformation: it operates on a vector $n$ (the normal to a ...
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Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
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Potential Energy in General Relativity

I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions: In ...
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Symmetrizing the Canonical Energy-Momentum Tensor

The Canonical energy momentum tensor is given by $$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$ A priori, there is no reason to ...
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Why is the (nonrelativistic) stress tensor linear and symmetric?

From wikipedia: "...the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it. ...The linear ...
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Showing symmetry of the stress tensor by applying divergence theorem to $\int\int_{\delta V(t)} \vec{x}\times \vec{t} dS$

I'm currently working through the symmetry of the stress tensor, in relation to viscous flow. I am looking at this by examining the conservation of angular momentum equation for a material volume ...
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What are the factors affecting the spacetime curvature?

Large masses in space as stars and planets cause a curvature in the spacetime fabric. What are the factors that affect this curvature? Is it only mass? And can we conclude these factors using Tensors? ...
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Why is gravity such a unique force?

My knowledge on this particular field of physics is very sketchy, but I frequently hear of a theoretical "graviton", the quantum of the gravitational field. So I guess most physicists' assumption is ...
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Energy-momentum tensor of Bosonic Ghost Action in String Theory

When quantizing bosonic string theory by means of the path integral, one inverts the Faddeev-Popov determinant by going to Grassmann variables, yielding: $$ S_{\mathrm{ghosts}} = ...
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Traceless of stress-energy tensor in $d=2$

This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function $$ S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right> $$ He then ...
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Constructing conserved current given the lagrangian

Consider the following Lagrangian for a massive vector field $A_{\mu}$ in Euclidean space time: $$\mathcal L = \frac{1}{4} F^{\alpha \beta}F_{\alpha \beta} + \frac{1}{2}m^2 A^{\alpha}A_{\alpha}$$ ...
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Source term of the Einstein field equation

My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
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Could Dust Equation of State have some negative pressure?

Traditionally the cosmological equation of state of cold matter (so-called dust) is simply: $$p = 0.$$ But, in Newtonian terms, each particle is gravitationally attracting every other particle. ...
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Formulation of general relativity

EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). ...
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Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
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Symmetry of stress-energy tensor

Why in the general case of classical field theory canonical stress-energy tensor doesn't have symmetry of the permutation of the indices? For explanation, let's have a "derivation" of an expression ...
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Why is the Maxwell Stress Tensor symmetric?

What is the physical meaning of the Maxwell Stress tensor symmetry?