# 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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### Relativity on a universal scale

Imagine there was a clock on a planet the same size as earth, travelling at the same speed through space, and that this planet was at the most distant part of the universe from earth. If we had a ...
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### Suggestions for GR solved problems books

Study Topic: General Relativity I'm looking for a recommendation for either a dedicated problems and solved solutions book or, failing that, a textbook with a separate comprehensive solutions manual....
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### Killing Vectors in Schwarzschild Metric

Given the Schwarzschild metric with $(-,+,+,+)$ signature, $$\text ds^2=-\left(1-\frac{2M}{r}\right)dt^2+\left(1-\frac{2M}{r}\right)^{-1}dr^2+r^2(d\theta^2+\sin^2\theta\,d\phi^2)$$ the lack of ...
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### Are gravitational time dilation and the time dilation in special relativity independent?

There are two kinds of time dilation: One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general ...
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### Centrifugal force in the two body problem?

In the two body problem, the Effective radial potential energy in general relativity is given by $$V(r)=-\frac{G M m}{r}+\frac{L^{2}}{2\mu r^{2}}-\frac{G(M+m)L^{2}}{c^{2}\mu r^{3}}$$ where the ...
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### A Calculation in Padmanabhan's Book

I have seen this in Padmanabhan's book. How can I verify this: d\Sigma_{mn}=\frac{1}{2!}\epsilon_{mnab}\frac{\partial(x^a,x^b)}{\partial(\theta,\varphi)}d\theta d\varphi=\epsilon_{mn\theta\varphi}r^...
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### $U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
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### What are Pre-requisites for General Relativity [duplicate]

I have a background in Electrical engineering. However, I have a passion for physics and want to do my Masters in Physics. I was hoping to do some sort of self - study in topics that I have not ...
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### If maximum speed limit $c$ is made infinite, will general theory of relativity become equivalent to Newton's gravitational theory?

We know that special relativity tends to become equivalent to classical theory of relativity as the speed limit of nature becomes infinite. If this happens, clock will tick at the same rate ...
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### Is a spacetime of constant positive curvature just a 4-hypersphere?

In discussions of basic cosmological models, I don't see "spacetime of constant positive curvature" described more simply as a "4-hypersphere". What am I missing?
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### Would a wormhole in space look like anything at all?

In movie "Interstallar", the wormhole is elaborately depicted as a sphere, complete with explanation about why it is spherical, and as it is approached, it looks like a sphere containing fabulous ...
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### Torsion-free, symmetric connection and non-coordinate basis

The torsion tensor is defined as (Hawking p.34) \mathbf{T}(\mathbf{X},\mathbf{Y}) = \nabla_{\mathbf{X}}\mathbf{Y} - \nabla_{\mathbf{Y}}\mathbf{X} - [\mathbf{X},\mathbf{Y}]. \end{...
I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in spacetime....