# 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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### Accretion disks on neutron star binaries

Why does hydrogen gas from accretion disks not constantly get sucked onto/into a neutron star or into a black hole? I understand that some gets sucked into the black hole and some may come down and ...
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### How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
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### How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
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### How to prove that a time-oriented spacetime possesses a nowhere vanishing timelike vector field?

Penrose gave a very brief proof to this question. Since the spacetime is paracompact, there exists a positive definite metric called $h_{ab}$. Then, the nowhere vanishing time-like vector field $V^a$ ...
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### Local symmetry and General Relativity

First I want to consider an example of 1D motion. Lagrange equation: $$\frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0$$ If we transform $L \rightarrow L+a$ ...
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### What is the effective physical difference between a massive region of a polarized vacuum and a region of curved space-time?

What is the effective physical difference between a large region of curved space-time and an equally large region of a polarized vacuum? Consider the fact that vacuum polarization amounts to an ...
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### $M^{+}_4$ Randall-Sundrum Brane Calculation

The basic Randall-Sundrum model is given by the metric, $$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$ where $\sigma$ ...
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### 'hypersurface orthogonal' component of covariant derivative of normal vector

I believe that answer to my question is rather trivial but I can't seem to get my head around it. In context of ADM formulation of gravity (or any other differential geometry context, I guess) the ...
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### General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
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### Metric to describe an expanding spacetime from coordinates reflecting the perspective of a local observer

The FLRW metric describes the metric expansion of spacetime from the perspective of comoving coordinates. Given the way this metric is usually formulated, comoving distances stay constant, and the ...
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### Questions about deduction the dual form of Frobenius's Theorem

I am reading Page 435, General Relativity by Wald. Let $T^*\subset V^*$ be a subspace of the dual tangent space of a manifold, $W\subset V$ be the subspace of the tangent space annihilated by $T^*$, ...
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### Topology of spacetime in 2+1 dimension

In the book Quantum Gravity in 2+1 dimension by S. Carlip, in the second chapter (section 2.1), he comments that a compact 3-manifold with a flat time orientable Lorentzian metric and a purely ...
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### Stringy corrections to Friedmann equation

Does anyone know a reference or a paper which discusses string theory correction to Friedmann equations?
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### How do we derive force/acceleration vectors from Einstein's field equations?

I'm new here and I don't have any formal experience in physics beyond A-level. I've been exploring an idea for a space sim game someone else is developing in which propulsion of a spacecraft is ...