# 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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### Why cant a repulsive event horizon of negative mass be theoretically constructed?

An event horizon appears in the Schwarzschild metric when considering a positive point mass in General Relativity. But for a negative point mass in the negative mass Schwarzschild metric, which ...
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### Conformal flatness of $\rm dS$ spacetime

There exists a flat slicing in the lower triangle area of the Penrose diagram of $\rm dS$ spacetime. To see this point, one introduces the planner coordinate, as defined in eq(13) of Les Houches ...
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### Electron Muon Scattering

I have been doing studying in advance for Dirac Equation and stumbled upon the math on calculating the spin-averaged amplitude $\bar{M}^{2}$ for the electron muon scattering process. Below is an ...
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### Killing vectors on the unit sphere

I am asked to find the Killing vector fields on $S^2$ where the line element is given by $ds^2=d\theta\otimes d\theta +\sin^2\theta d\phi\otimes d\phi$. I know how to solve this problem by considering ...
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### Continuity equation as a four-divergence. Possible misunderstanding of contravariance, covariance, or metric signature

Context I am studying electromagnetic quantities through the framework of special relativity. I find it notation heavy and the issue of tensors is something I am still not fully grasping. The ...
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### Local Supersymmetry and Space-time Metric

So following from Simple Supergravity (arxiv:2212.10044), on page 5, it's written that Only the spacetime metric can couple to the energy-momentum tensor... Can anyone explain why it must be the ...
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### Connection between pseudometric and Einstein elevator

I have a hard time understanding GR. I understand a lot (from a math point) about (pseudo)Riemannian manifolds, and I also learned about Einstein's elevator thought experiment. So let me elaborate: ...
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### How is the Ricci scalar the trace of the Ricci tensor?

The Ricci scalar is the uncontracted version of the Ricci tensor $R=R^{\mu}_{\mu}=g^{\mu\nu}R_{\mu\nu}$. Carrol describes the Ricci scalar as being the trace of the Ricci tensor, but I do not ...
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### Can $\mathbb{R}^4$ be globally equipped with a non-trivial non-singular Ricci-flat metric?

I'm self-studying general relativity. I just learned the Schwarzschild metric, which is defined on $\mathbb{R}\times (E^3-O)$. So I got a natural question: does there exist a nontrivial solution (...
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### Confusion about choosing an Euclidean world sheet metric in String Theory path integral

When it comes to construct a well-defined path integral for the Polyakov action in Bosonic String Theory, most authors assume that the world sheet metric $g$ is Riemannian (i.e. it has Euclidean ...
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### Zero Einstein Tensor in 4D

In 2D the Einstein tensor is always zero, and we can easily get solution with non-zero Ricci tensor but zero Einstein tensor. But is it possible in 4D? Can we get a space-time with zero Einstein ...
1 vote
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### Static spherically symmetric spacetimes

I would like to better understand a hypothesis that Wald uses to derive the general local formula of a static spherically symmetric spacetime. A spacetime is said to be spherically symmetric if its ...
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