# 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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### For the Schwarzschild metric, are the values of the Ricci tensor and Ricci scalars always zero?

If we use the Schwarzschild metric to solve the Einstein field equations, would the values of the Ricci tensor and scalars always be zero?
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### Expectation value of stress-energy tensor

In the following page, notes by \textit{Brout}, how they are calculating 2.86 first line to second line?
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### Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter?

Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter? If so, can we extend Einstein field equations globally relating global spacetime curvature to ...
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### Understanding EFE: RHS linear, LHS not?

Einstein's field equations are nonlinear. That means it is not allowed to add up the metric tensors. However, on the RHS of the field equations, there is only the stress-energy-momentum tensor, and it ...
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### Energy-momentum tensor of a perfect fluid flowing at the speed of light?

The general energy-momentum tensor for a fluid is given by (working with $c=1$ convention) $$$$\label{T}\tag{1}T^{\mu\nu}=\left(\rho+p\right)U^\mu U^\nu+p g^{\mu\nu}$$$$ with ...
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### Covariant vs. contravariant definition of the Energy-Momentum tensor

I have a question regarding the definition of the energy-momentum tensor. I've seen it defined as a (2,0) tensor, so it has 2 upper indices $T^{ab}$, but many times it is written as a (0,2) tensor ...
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### Null vectors that aren't the zero vector in general relativity?

So I was trying to understand the null energy condition of $T_{μν}k^μk^ν≥0$ Where $k$ is an "arbitrary future-directed null vector" and couldn't really wrap my head around how the $k$ is ...
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Radiation pressures mathematical expression according to Wikipedia is, $\frac{1}{\mu_0 c}\vec{E} × \vec{B}$ "Radiation pressure is the mechanical pressure(force/area) exerted upon any surface due ...
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### How to interpret the Lagrangian $\int d^3x \sqrt {-g} R$?

In GR, one of the degrees of freedom is that of the metric tensor. That means a tensor $g_{ab}$ at each point of space. The other degree of freedom is that of the energy distribution. That's also a ...
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### Will an object with linear velocity in outer space experience frame dragging effects?

Will an object moving non-accelerated in outer space experience frame-dragging? It seems the mass contributions to the strdss-energy-momentum tensor are distributed spherically symmetrical, and don't ...
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### How to find the energy-momentum tensor of a free relativistic particle from its lagrangian?

Consider a free relativistic particle in Minkowski spacetime. Its standard action is the following, where $\sigma$ is an arbitrary parametrization ($\tau$ is the particle's proper time. I'm using ...
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### Why this boundary term could be ignored for a free relativistic particle?

How can we justify that the boundary integral we get from the following could be ignored, when we want to find the equation of motion? I consider the energy-momentum of a free particle in special ...
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