# Tag Info

• 38.5k

### Does the stress energy tensor scale with the metric tensor?

What you're asking about is a specific case of Weyl transformations of the form $$g_{ab} \rightarrow e^{-2\phi(x)}g_{ab}$$ where $\phi$ is a constant. Under these, the Ricci scalar is not invariant (...
• 2,839

### Understanding EFE: RHS linear, LHS not?

This is just a small comment to buttress Andrew's answer (since it was a long string of comments on his answer!). Let us review the definitions of basic geometric gadgets used in Einstein's field ...
• 2,645
Accepted

### How can any spatially extended object have 4-momentum assigned?

Consider a particular inertial reference frame with coordinates $\{t, x, y, z\}$, and let $t^a$, $x^a$, $y^a$, and $z^a$ be their corresponding orthonormal basis vectors. The set of events in ...
• 37.1k
1 vote
Accepted

### Linear Momentum in General Relativity

Is there a metric that describes this case? Yes. It is the Schwarzschild metric (valid outside of the gravitating body if we are talking about something like a star). When written in the form where ...
• 12.5k
1 vote

To supplement Eletie's answer, note that under the transformation $g\mapsto \lambda g$ with $\lambda$ an $\mathbb R$-valued constant, the Christoffel symbols remain unchanged because $\Gamma \sim g^{-... • 50.8k 1 vote Accepted ### Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter? Yes, they cannot be extended to relate global curvature to global energy-momentum, not in general at least. You can see this by noting that the Einstein Field Equations can be derived by demanding ... • 1,964 1 vote Accepted ### Energy-momentum tensor of a perfect fluid flowing at the speed of light? Once the radiation fluid is traveling at the speed of light in a particular spatial direction, the situation effectively becomes equivalent to a mixture of plane waves of light traveling in the same ... • 1,449 1 vote ### Covariant vs. contravariant definition of the Energy-Momentum tensor The metric$g_{\mu\nu}$can be used to raise and lower indices. In this case you are lowering the indices on the SEM tensor, that is converting it from contravariant to covariant. So the answer is ... • 313 1 vote ### Understanding the meaning of (and using) Maxwell Stress Tensor Field momentum:$\mu_0 \epsilon_0 \vec{S}\$ is the momentum density of the field. Integrating this about a volume, finds the TOTAL field momentum in that volume. The rate of change of this, is the ...
• 3,705

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