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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Problems of General Relativity on small and large scales [duplicate]

As far as I know, the most important problem of GR on large scales is the cosmological constant problem which in some manner can be thought of as a dark energy problem (please correct me if I am ...
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If there is a point in a past set, does its chronological future interset a future set?

This post concerns the causality of spacetime $\mathcal M$. A future set $F$ is defined to be the chronological future of some set $S\in \mathcal M$, ie., $F=I^+[S]$. Similiarly, a past set ...
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Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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Hermiticity of Dirac operator in curved spacetime

The Dirac Lagrangian in curved spacetime is usually given by \begin{equation} \mathcal{L} = i\bar{\Psi}\gamma^a e^{\mu}_a(\partial_\mu + \frac{1}{4}\omega_{\mu bc}\gamma^b\gamma^c)\Psi \end{equation} ...
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GR time dilation cares only about local curvature, right?

Regarding this remark on Worldbuilding SE and the discussion leading up to it: Can someone properly knowledgeable on the subject please explain whether the time dilation due to being in a gravitation ...
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Event horizon from the metric

Let us suppose we have a metric of this form $$ds^2=-A(r)dt^2+\frac{dr^2}{B(r)}+r^2d\Omega^2$$ In all documents I can read, I've seen that the event horizon is defined by considering $A(r)=0$ But I ...
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Does General Relativity say that the Laws of Physics are the same in all Reference Frames?

Most texts on General Relativity seem to imply that Einstein generalized the Relativity Principle (that all reference frames are equivalent) to include changes in velocity (accelerations); but then go ...
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The equivalence principle and experiments concerning it?

Imagine that we are in a rocket accelerating with some magnitude $a_1 = dx^2/d^2t$, also imagine that we have a stationary rocket ship in close proximity to ours, stationary relative to our reference ...
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Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold?

For $R_{\mu \nu \sigma \rho}$ the Riemann-tensor and $R$ the Ricci-scalar: Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold? Or is there any way to relate $R$ approximately ...
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Cosmological constant in General Relativity [duplicate]

According to my GR notes the cosmological constant can be thought of as a vacuum energy much in the same way as the ground state of the harmonic oscillator. The notes claim that the regularised energy ...
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What is the conformal mode of a metric?

I have a problem in terminology. This article talks about the conformal mode of a physical metric. I know what a conformal transformation is. But what is the conformal mode of a metric?
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Interpretation of black hole area

I'm studying properties of Kerr spacetimes and a lot of fuss is made about area of BH. It is defined to be integral of area element on event horizon $r=r_+$, $t=const.$ where $r_+$ is radial ...
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Does the spin of a particle change if observed from an accelerating reference frame?

If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable. Let's arbitrarily choose the ...
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How do gravitational waves work without internal tension?

One implication of general relativity is the concept of gravitational waves or gravitational radiation, ripples in spacetime thought to travel at speeds close to the speed of light. As far as I have ...