Questions tagged [general-relativity]

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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We all accept/believe in C. But what happens when light travels away from the center of gravity of a heavy star? Does it slow down?

I'm basically trying to understand a mysterious characteristic of the universe. Why light has to travel at C. I understand and accept that from experiment. Not arguing that it does not. Just saying ...
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Is the relativistic time dilation compatible with the gravitational field of a moving massive planet?

Assume that a satellite orbits a massive planet/star at a distance $r^\prime$ away from its center in a circular path in plane $x^\prime y^\prime$. Suppose that the gravitational field is $g^\prime$ ...
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How the variation of Gauss Bonnet term is done?

I am trying to do the variation of Gauss Bonnet Invariant which is $G=R^2+R_{abcd}R^{abcd}-4R_{ab}R^{ab}$ and having problem in doing the variation of $δ(R_{abcd}R^{abcd})$. Can anyone please give ...
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Motivation for tensor theory of gravity

In class we were shown that $$\rho = \frac{dm}{dV}$$ has the transformation properties of the 00 component of a rank 2 tensor. So we'd like to turn the classical Poisson equation for gravity into a ...
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Gravitational wave energy fluxes and bracket averaging notation

Typically the rate of energy loss due to gravitational waves is given in the form (e.g. MTW or Eq 33 of these notes), $$\dot{E} = - \frac{1}{5} \langle \dddot{I}_{jk} \dddot{I}_{jk} \rangle$$ where ...
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Comparing Theory of Relativity with Newtonian gravity [duplicate]

How does Einstein's General Theory of Relativity compare with Newtonian gravity? How does the curvature of spacetime affect both gravity and the path of light in a planetary system?
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Is there somesort of “recipe” to check if an spacetime exibit the Unruh effect?

Firstly I don't know for sure if this question makes a solid sense, concerning the physical phenomena. I) Unruh Effect Now, we have then the Unruh effect which appears just by considering the ...
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Undertsanding gravitational time dilation in terms of four-vectors

I am struggling to understand how to calculate gravitational time dilation using four-vectors, based on my understanding of them. Specifically, I would appreciate if someone could point out the ...
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Why covariant derivative is partial derivative in SR?

I'm new in these topics and i've been confuse at some relations between the limit of SR for GR. In cartesian coordinates, basis do not change, so \begin{equation}\Gamma^{\mu}_{\alpha\beta}=0 \quad \...
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In a gravitational wave, why is the effect on path length due to the change in path negligible?

This is about Example 16.1 of Hartle's Gravity book, which considers a wave traveling along the $z$-direction given by $$ds^2=-dt^2+(1+f(t-z))dx^2+(1-f(t-z))dy^2+dz^2,$$ where $f(t-z)\ll1$. Of this ...
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If I surrounded a black hole with gravitometers and observed the gravitational field as mass passed the event horizon, what would I observe?

By surrounding a black hole with gravitometers I would be able to get a 3-D map of the gravitational field. If I observed this field as an object approaches the event horizon, what would I see? Would ...
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Basic question about units of velocity and speed of a curve on a smooth manifold

Frederic Schuller says that velocity has units in Hertz in The WE-Heraeus International Winter School on Gravity and Light. He says: \begin{align} [v^a]&=\frac 1 T \\ [g_{ab}]&=L^2 \\ \Big[\...
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Changes to a Length of Physical Ruler Caused by Gravity vs Caused by Cosmological Expansion of Space

I read here (Feynmann Lectures, Lecture 42) that "Just as time scales change from place to place in a gravitational field, so do also the length scales. Rulers change lengths as you move around." (...