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Results tagged with metric-tensor
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user 68519
The variables used in general relativity to describe the shape of spacetime. If your question is about metric units, use the tag "units", and/or "si-units" if it is about the SI system specifically.
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Why is the first component of the energy-momentum tensor $-p_a v^a$?
A single particle of mass $m$ travels along a geodesic curve in flat spacetime. A tangent vector $u^a$ to this geodesic, parameterised by the parameter $\tau = \int \left( \eta_{\mu \nu}u^\mu u^\nu \r …
- 278
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Condition for quadratic correction to first-order perturbation of metric
In Wald's book on General Relativity, the linearized Einstein tensor $G^{(1)}_{ab}$ can be obtained by substituting $g_{ab} = \eta_{ab} + \gamma_{ab}$ in the Einstein equation and ignoring terms that …
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How do you obtain the coordinates of 3D space from the FLRW metric?
Under the assumptions of homogeneity and isotropy, it can be deduced that for a one-parameter family of spacelike surfaces folliating spacetime, the curvature within each such surface is constant. Thi …
- 278
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Why does this falsely lead to $g_{\mu \nu}$ always being the identity map?
So I posted a question about the tetrad basis but later realised that there is a more fundamental, underlying question that is better suited here.
I’m using abstract index notation to denote all tenso …
- 278
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Extra factor in Fourier transform of $\bar{\gamma}_{\mu \nu}$
In the weak gravity limit (and with proper gauge transformations), the linearized Einstein equation is given by:
$$
\partial^c \partial_c \bar\gamma_{ab} = -16 \pi T_{ab}\tag{4.4.12}
$$
where $$g_{ab} …
- 278