# Questions tagged [metric-tensor]

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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### Question on Painlevé-Gullstrand coordinates

A known set of coordinates used for the Schwarzschild metric is the Painlevé-Gullstrand coordinates. They consist in performing a change from coordinate time $t$ to the proper time $T$ of radially ...
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### Spacetime diagram for static weak field metric

Can anyone draw/provide links to the spacetime diagram for the static weak field metric (where Newton's law applies)?
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### Deriving Einstein-Rosen Bridge

I know that an einstein rosen bridge is derived by a coordinate transformation on the schwarzschild metric, but I can't find much on it online, could someone please show how to change the metric into ...
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### Question on the Einstein-Hilbert action

Does it make sense to write that the Einstein-Hilbert action as S=\int\mathcal{L}\left(g^{\mu\nu},\partial^{\lambda}g^{\mu\nu}\right)\sqrt{-g}\,\mathrm{d}^4x=\frac{1}{2\kappa}\int R\,\...
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### Components of a vector after translation

If you have a vector expressed in curvilinear coordinates and you translate it to a different point in space, the components of the vector will change to ensure that it maintains its geometric ...
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### Why is spacetime not Riemannian?

I apologize if this is a naïve question. I'm a mathematician with, essentially, no upper-level physics knowledge. From the little I've read, it seems that spacetime is Lorentzian. Unfortunately, the ...
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### Is Birkhoff's Theorem Valid in Higher Dimensions?

I have seen a question here on PSE asking the same thing, but it has no answers. To reformulate the question slightly differently, suppose you have a general spherically symmetric metric in $(1+D)$ ...
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### Zamolodchikov metric and coupling-dependent field rescalings

this is my first post/question, so I apologize in advance for any mistakes in phrasing or format or anything else. Consider a conformal field theory (CFT) with exactly marginal deformations described ...
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### Perturbation of the energy-momentum tensor: mistake in my computations or in the book?

In the book Cosmology - S. Weinberg eqauation $(5.1.28)$ is $$\delta T^{\mu}_{\;\;\nu} = \bar{g}^{\mu\lambda} [\delta T_{\lambda\nu} - h_{\lambda\kappa} \bar{T}^{\kappa}_{\;\;\nu} ] \tag{5.1.28}$$ ...
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### Confusion with certain aspects of the Equivalence Principle

I took a course on GR and I am revising it after a while. I am heavily confused about the equivalence principle. Consider the following two statements: On a Riemannian manifold, we can always choose ...