# Tagged Questions

A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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### Is it possible to define a symmetry group for the Einstein metric?

I was just wondering if there exists a group of transformations that act on the metric such that the EFE are invariant. At first I thought it would be the group of 2nd roots of unity. That is, the set ...
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### The spatial Schwarzschild metric

The Schwarzschild spacetime is defined by the following line element \begin{equation*} ds^2 = - \left( 1 - \frac{2m}{r} \right)dt^2 + \frac{1}{1-\frac{2m}{r}}dr^2 + r^2 d\theta^2 + r^2\sin \theta^2 d\...
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### Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question: If the proper time $\tau$ is infinite for a timelike geodesic, does it mean ...
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### Variation of Bazanski Lagrangian

The Bazanski Lagrangian is defined as $$L=g_{\alpha \beta }U^{\alpha }\frac{D\psi ^{\beta }}{Ds}$$ and $$U^{\alpha }=\frac{\mathrm{d} x^{\alpha }}{\mathrm{d} s}$$ $x^{\alpha }$ is the ...
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### Equation of state of a universe full electrons

If I have a universe full of nothing but (slow moving) electrons, what would the equation of state ($w$, from $p=w\rho$) be? I think it would be incorrect to say that the electrons should be treated ...
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### Any textbook about non-renormalizability of gravity?

I have learned general relativity in a graduate-level. My knowledge about QFT is very rudimentary. But, I need to learn about non-renormalizability of gravity. I have these questions. Is there any ...
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### Variation of quadratic term in modified Einstein-Hilbert actions

In the context of mimetic gravity at some point one try to add to an already modified Einstein-Hilbert action also a term like $$S_\chi=\int\,d^4x\,\sqrt{-g}\frac{1}{2}\gamma\chi^2,\qquad(\star)$$ ...
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### Compactly generated vs. compactly constructed causality violating region?

I am currently trying to grasp the nuance between a compactly generated future Cauchy horizon (as per Hawking's chronological protection conjecture) and a compactly constructed causality violating ...
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### Normal of a null surface and null junction conditions in general relativity

I am trying to use the null junction formalism in general relativity (as explained in eg http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.43.3763&rep=rep1&type=pdf, "Junctions and thin ...
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### Would a very long massive rod exhibit a large deviation from Newtonian gravity (specifically a deficit angle rather than 1/r force)?

In General Relativity the metric corresponding to an infinitely long massive rod is flat but with a deficit angle. It exhibits a very large deviation from Newtonian gravity in all regions of space in ...