# 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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### Basic understanding of Gravity Wells

In all the diagrams I have seen, a large astronomical body eg. a planet or star, shows its gravity well as one dimensional in spacetime. My basic question is: Is it truly one dimensional or multi-...
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### Why would time distorsion be greater than space distorsion? [closed]

So, I'm reading The Hidden Reality by Brian Greene, and on page 31, he does state in a note that time distorsion has a bigger influence than space distorsion? I have trouble understanding that, since ...
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### The Circular Orbital Velocity Relative to a Stationary Observer in Schwarzschild Geometry [closed]

Relative to a stationary observer (constantly accelerating to maintain a fixed radius) what would be the velocity measured of an object in circular orbit. I've tried using J B Hartle (9.47) and (9.48) ...
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### Merging timelike and spacelike surfaces

In the following paper there is a statement which says: We propose to determine the boundary length by merging smoothly the timelike and spacelike surfaces in such a way that they are homologous to ...
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### GW luminosity depends on the 3rd time derivative but quadrupole formula depends on the 2nd time derivative?

The quadrupole formula for GW emission (see here) states that the metric perturbation is given by: \begin{align} \bar{h}_{ij}(t,r) = \frac{2G}{c^4 r} \ddot{I}_{ij}(t - r/c) \end{align} This ...
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### What metric to use for this dark matter simulation?

I am reading this paper https://arxiv.org/abs/1901.08064 which uses the GR version of euler equations in fluid dynamic to simulate the evolution of a perfect fluid system. (PDF) and this is the paper ...
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### Spacetime coordinates 4-dimensional vs curvature of space time? [closed]

what is the difference between spacetime coordinates 4-dimensional and curvature of space time I dont know the difference between both of them
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### Does Birkhoff's theorem work just as well in the non-geometric approach to general relativity?

Does Birkhoff's theorem work just as well in the non-geometric approach to general relativity? My guess is, that it should due to the equivalence with the geometric approach. On the other hand, ...
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### Why different versions of the Schwarzschild metric online?

I started studying the Schwarzschild metric and have seen multiple versions of the metric online; specifically different versions of the Schwarzschild radius. In some cases it is $\frac{2GM}{c^2}$, ...
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### Understanding Feynman: why gravity is not a spin-0 theory?

I'm struggling to understand a certain paragraph in Feynman's "lectures on gravitation". It's lecture 3, why gravity cannot be a spin-0 theory. Here's the text: The rejection of spin-zero ...
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### Wormholes in general relativity

From what I understand there is no physical evidence for wormholes, but are their certain solutions to the einstein field equations that allow for them?
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### Why does null geodesic incompleteness indicate the breakdown of GR?

If a spacetime in general relativity (GR) is null or timelike geodesically incomplete, it is said to be singular (more precisely, there is a more general notion of a "b-incompleteness" of ...
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### When we write down the FLRW metric,what are the basis vector or coordiante lines of the coordiante system?

When we consider the coordinate system,it seems we can always ask for how the curvlinear coordinate lines looks like. So if the universe started evluting from a point,then whether the coordinate ...
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### Why do the Schwarzschild and FLRW metrics treat curvature so differently

In the Schwarzschild metric, which describes a black hole, when a massive body crosses the event horizon, the radius and curvature of the black hole immediately increase. The increase in curvature is ...
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### What's the relevance of geometric rigidity/flexibility to physics?

I'm currently working on a mathematics research problem in differential geometry that deals with the rigidity of closed manifolds described by non-trivial induced metrics. I'm curious what the ...
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### What is the qualitative difference between the (generalized) Israel theorem and the no-hair theorem?

I know that the Israel theorem accounts for only non-rotating, non-electrically charged black holes, but as I understand the theorem was then generalized for rotating and charged black holes. And, as ...
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### Do gravitational waves cause matter to radiate?

Gravitational waves distort the "fabric" of spacetime. In doing so, it seems they can cause particles to accelerate. On the other hand, textbook electromagnetism predicts accelerated charges ...
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### "A coordinate transformation changes components, but not one-forms themselves" [closed]

I'm very puzzled by a statement made by Sean Carroll in his Spacetime and Geometry: An Introduction to General Relativity textbook. Discussing tensor densities at page 89, he says: "But the ...
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### Calculating Ricci tensor given the metric - undergraduate GR [closed]

I’ve been trying to solve the following problem: Consider an $(N + n + 1)$-dimensional spacetime with coordinates $\{t, x^I, y^i\}$, where $I$ goes from 1 to $N$ and $i$ goes from 1 to $n$. Let the ...
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### What specific renormalized Lagrangian is used for quantum gravity of GR?

I have heard that the Lagrangian that is used for quantum gravity but produces a theory that requires infinite constants to be renormalized. This Lagrangian is supposed to be a linearization of the ...
1 vote
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### Conformal compactification of Minkowski spacetimes

Let's say we compactify the Minkowski space-time through the following coordinate transformation: $$u=t-r, \\ \Omega=\frac{1}{r},\\ \theta=\theta,\\ \phi=\phi.$$ The conformally rescaled unphysical ...
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### Can Entropy be considered a kind of Affine Parameter?

In general relativity and differential geometry, an affine parameter is used to parameterize geodesics such that the geodesic equation $\nabla_{\mathbf{T}} \mathbf{T} = 0$ holds true, and the ...
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### Why does $a\cos{\theta}$ represent rotation in the Kerr metric?

In any introductory book to GR where the Kerr metric is reviewed, they all apply transformations of the form: $$cu' = cu + ia\cos\theta;\text{ } r' = r + ia\cos\theta$$ In the end, the result ...
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### Is Friedmann's equation compatible with the cosmological principle?

The first term in Friedmann's equation is $\frac{8\pi G \rho}{3}$, the CDM component. Here we recognize $4\pi G \rho$, which is the $\nabla \cdot(-g)$ of a body of density $\rho$. If, instead, we ...
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### Global Hyperbolicity of Spacetimes implying Connectedness

I am currently working on a problem and right now I want to show that the global hyperbolicity of a spacetime M implies, that M is connected. Therefore, I assumed the following: We could write $M$ as ...
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### Prove a four-velocity vector lies inside of the light cone; do I just need to prove that the four-velocity is a timelike vector?

New to relativity; and I'm reading the Hartle books, on page 144; The questions asks to show that, at every point along the curve $x_s(t)$, the four-velocity of the ship lies inside the forward light ...
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### Dictionary between light propagation in curved spacetime and anisotropic media - with focus on Shapiro delay in weak fields

I am looking for a mathematical dictionary to translate from light propagation in curved spacetime to light propagation in anisotropic media. Special focus is on the optical path length in the context ...
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