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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Derivation of Einstein-Cartan (EC) action for parametrized connection $A$ & introduction of torsion
I have some trouble with one missing step when I want to get the teleparallel action from general EC theory, which I am not fully understanding.
The starting form of action is:
$$
S_{EC}=-\frac{1}{8\...
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Where is the mass in a Black Hole without a "central" curvature singularity?
Not all black holes have a curvature singularity at their center (an example). But in principle, I thought that the curvature singularity was a direct result of the fact that the mass is concentrated ...
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How to properly combine kinetic and gravitational time dilation effect?
I developed a time dilation calculator that includes both kinetic (Lorentz Factor) and gravitational (Schwarzschild Metric Formula) factors to assess the time difference between Earth and satellites. ...
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Do you always experience the gravitational influence of other mass as you see them in your frame?
You see a galaxy far away. That galaxy is attracting you with a certain amount of gravity. I'm wondering if the gravity influence of the galaxy on you, as measured by you, always ends up being what ...
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Energy-momentum tensor and equation of motion in Einstein-Dilaton theory
I am following this paper (see eq. 19-22) and trying to derive the equation of corresponding to Einstein-Dilaton gravity (ignoring the Maxwell part for now)
\begin{align}
S_{\text{E-D}} = \int d^4 ...
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Tug of war between observers in frames with different rate of time
You have a very dense hollow sphere of matter. Observer A is inside the sphere inside a rocket. Observer B is in an identical rocket outside the sphere where the ring's gravity is negligible. They are ...
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Checking inverse metric and Christoffel symbols for the Kerr metric against references
I am trying to cross-check the Christoffel symbols and other very laborious geometric components in several metrics. In particular the Kerr metric is notoriously complex and results in expressions ...
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Independence of the equations resulting from the action principle $\delta (I_{\text{gravity}} + I_{\text{other fields}}) = 0$
In Dirac's "GTR", Chap. $30$, he discusses the "comprehensive action principle" and shows that variation of the combined action of the Hilbert-Einstein action plus all other matter-...
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Saddle Shaped Universe
The universe, as described by FLRW metric, if $k = -1$ is clearly a 2 sheet 3-hyperboloid described by $x^2+y^2+z^2-w^2=-R^2$. So where does the more common saddle shaped picture of the open universe ...
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Do clocks tick faster when gravitational forces are weaker?
A professor last year taught us that "gravity slows clocks," when teaching about the relationship between gravity and time. This led me to think about places, such as intergalactic space, ...
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How can I visualise a sphere with a negative radius? [closed]
I want to visualise the shape of the sphere , will having a negative radius turn the inside of the sphere outside or something other will happen ?
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Action principle dependent on spacetime-topology?
Consider the Lagrangian density
$$L(\phi, \nabla \phi, g) = g^{\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi$$
If one varies the action as usual, then one finds the equation
$$\delta S = \int_{\mathcal{...
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What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$
What's the difference? $$\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$$
In John Dirk Walecka's book 'Introduction to General Relativity',...
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Radiation energy and momentum relation [duplicate]
Why is $\rho = 3p$ for radiation? What is the intuition behind this? If we had only 2 spatial dimentions, would it be $\rho = 2p$?
(I came across this relation while studying the state of the universe,...
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Embedding diagram of $\phi=\mathrm{constant}$ surface in cylindrically symmetric spacetime
I'm trying to generate an embedding diagram for the $\phi=\mathrm{constant}$ hypersurface in a cylindrically symmetric spacetime. I think I'm supposed to start with $$A(p,z)dp^2+A(p,z)dz^2=dw^2+dp^2+...
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