# What is Stress-energy tensor: Definition and 98 Discussions

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

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1. ### I Stress-energy tensor and energy/momentum conservation clarification

I've been working through Bernard Schutz's book on GR and have run into some confusion in chapter 4 problem 20 part b. In this chapter, the stress-energy tensor for a general fluid was introduced and was used to derive the general conservation law for energy/momentum, where we found that...
2. ### I Diagonal Matrix of Stress-Energy Tensor: Why?

I came across a statement in《A First Course in General Relativity》:“The only matrix diagonal in all frames is a multiple of the identity：all its diagonal terms are equal.”Why?I don’t remember this conclusion in linear algebra.The preceding part of this sentence is:Viscosity is a force parallel...
3. ### SH2372 General Relativity - Lecture 7

0:00 Gravitational time dilation 12:06 Gravitational redshift 14:43 Dynamics of spacetime 34:17 Matter in spacetime 51:07 The stress-energy tensor 1:03:00 Ideal fluids
4. ### I Question about Stress-Energy Tensor: A First Course in GR

I came across a statement in《A First Course in General Relativity》on page 97 which confused me.It read:"if the forces are perpendicular to the interfaces,then##T^i{^j}##will be zero unless ##i=j##". Where the ##T## is stress-energy tensor,##T^i{^j}##is the flux of i momentum across the j surface.
5. ### I Yang-Mills Stress-Energy Tensor Explained

It's given as ##T_{\mu \nu} = - \mathrm{tr}(F_{\mu \lambda} {F_{\nu}}^{\lambda} - \frac{1}{4} g_{\mu \nu} F_{\alpha \beta} F^{\alpha \beta})##. Can somebody explain the notation, i.e. what is the meaning here of the trace? (usually I would interpret the trace of a matrix as the number...
6. ### B Understanding the Stress-Energy Tensor & Solar Mass in General Relativity

In the test of General Relativity by perihelion motion of mercury, the stress-energy tensor is set to 0 in Schwarzschild solution. Then, is the curvature caused by solar mass, or by the 0 stress-energy? Or, do we consider solar mass as the gravitating mass? Or the 0 stress-energy the gravitating...
7. ### Stress-energy tensor for a rotating sphere

The answer with no details is given by First, I considered a spherical shell because I thought the velocities at different radius ##r## will be different and hence the four-momentum will be different, as well. Then, I writed down the linear momenta by $$\epsilon^{ijk} r_i p_j = L_k$$ with...
8. ### B Special Cases of Stress-Energy Tensor in GR

Background and Motivation The stress energy tensor of general relativity, as conventionally defined, has sixteen components. One of those component, conventionally component T00, also called ρ, is mass-energy density, including the E=mc2 conversion for electromagnetic fields. The other...
9. ### I Stress-Energy Tensor for Dust

Given the action ##S =-\sum m_q \int \sqrt{g_{\mu\nu}[x_q(\lambda)]\dot{x}^\mu_q(\lambda)\dot{x}^\nu_q(\lambda)} d\lambda## The Energy-Momentum Tensor (EMT) is defined by the variation of the metric $$\delta S = \frac{1}{2}\int T_{\mu\nu} \delta g^{\mu\nu} \sqrt{g} d^4x$$ Then I use two...
10. ### I Understanding the Stress-Energy Tensor in Special Relativity

Hello, I try to understand how to get the last relation below ##(3)## ( from stress energy tensor in special relativity - Wikipedia ). I understand how to get equation ##(1)## but I don't grasp how to make appear the gradient operator in the dot product and the divergence operator in the...
11. ### A Can you numerically calculate the stress-energy tensor from the metric?

About 10 years ago I worked on a project where I took a mater distribution and numerically solved for spatial curvature. Can this be done in the opposite direction? Can anybody point me to a resource that would allow me to calculate matter distributions when the metric is specified? What are...

47. ### Why is the stress-energy tensor symmetric?

If we use the "flux of 4-momentum" definition of the stress-energy tensor, it's not clear to me why it should be symmetric. Ie, why should ##T^{01}## (the flux of energy in the x-direction) be equal to ##T^{10}## (the flux of the x-component of momentum in the time direction)?
48. ### Stress-energy tensor for a single photon

Hi, I'm trying to write down the stress-energy tensor for a single photon in GR, but I'm running into trouble with its transformation properties. I'll demonstrate what I do quickly and then illustrate the problem. Given a photon with wavevector p, we write {\bf T} = \int \frac{\mathrm{d}^3...
49. ### Maxwell's equations from divergence of stress-energy tensor?

If I start with the stress-energy tensor T^{\mu\nu} of the electromagnetic field and then apply energy-momentum conservation \partial_\mu T^{\mu\nu}=0, I get a whole bunch of messy stuff, but, e.g., with \nu=x part of it looks like -E_x \nabla\cdot E, which would vanish according to Maxwell's...
50. ### Stress-energy tensor (in SR)

According to Wikipedia, This definition doesn't sit well with me. Flux is defined as the rate that something passes through an infinitesimal surface, divided by the infinitesimal area of that surface. For example, the current flux (or current density), when dotted with a unit vector, gives...