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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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Is there some physical interpretation of the parallel exterior region?

Let the maximal extension of the Schwarzschild spacetime be given. It admits as coordinates the Kruskal-Szekeres coordinates $(T,X,\theta,\phi)$ with $$T^2-X^2<1$$ since the singularity occurs at $...
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Relationship between freefall velocity time dilation and gravitational time dilation in a Schwarzschild metric

If you drop an object into a gravitational field, is its final velocity equal to what it would have to be in flat space in order to generate the same time dilation that you get at a given radius for ...
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Is time passing really differs on other planets/in interstellar?

I am aware of the idea of time dilation (which I, by the way, asked another question about) on speeds, that get close to the speed of light. Though, I wonder what other (if any) forces and laws affect ...
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Time dilation caused by gravity and special relativistic velocity

I am working on an exercise for my Relativity class. The exercise is: Two atomic clocks are transported in two aeroplanes once around the Earth in either eastern or western direction. For ...
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Meaning of flux 2-integral

Can someone please explain the meaning of flux 2-integral in this sentence: Mass is evaluated as a flux 2-integral at the asymptotic infinity. For asymptotic infinity, I believe it is as ...
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Question about inertial frames and geodesics

Consider the following text: In Newtonian Mechanics the first law is given by: $$\Big[m \Big(\frac{d^{2}x^{a}}{dt^{2}} + \Gamma^{a}_{bc}\frac{dx^{b}}{dt}\frac{dx^{c}}{dt}\Big)\Big]\frac{\partial}{\...
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Differential forms manipulation in Cartan's formalism

this may be a silly question but I'm not seeing any easy answer. Right now I'm dealing with the condition of zero-torsion of the spin connection in General Relativity: $$ 0=de^a +\omega{^a_b}\wedge e^...
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Is the spacetime curvature of the Earth the reason for the orbiting of the Moon around the Earth?

The planets revolve around the Sun due to its spacetime curvature of gravity. Does the same apply to the satellites of the planets?
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Problems 4.1 and 4.2 (Sean Carroll, General Relativity) [on hold]

Well, I can not solve these two questions. Could someone help me solve them? (Exercise 4.1) The Lagrange density for electromagnetism in curved space is $$\mathcal{L}=\sqrt{-g}\left(-\frac{1}{4}F^{\mu ...
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Free-falling stationary observer in curved spacetime?

Let us consider the pseudo-riemannian manifold $(\mathcal{M},g)$ with $\mathcal{M}=\mathbb{R}\times\mathcal{N}$ with $\mathcal{N}$ being a maximally symmetric, 3-dimensional riemannian manifold and $...
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3-dim Hyperboloid harmonic

I don't know how to derive this eigen value $L^2 Y_{plm} = (1+p^2)Y_{plm}$ In this equation $p$ is real positive number. reference: D. Gromes, H. J. Rothe and B. Stech, Nucl. Phys. B75, 313 (1973).
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Are singularities' behaviour really unpredictable?

If a real/true singularity existed our models and theories would become useless to predict what would happen in that singularity. For example if naked singularities really existed, we could not ...
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Distinguishing between matrix forms when reordering indices of tensors

I'm studying general relativity and tensors. It seems that in the cooridnate independent form of the tensor, the order of indices matters even between an upper and lower index. For example, in general,...
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Solving a 2-particle gravitational problem with General Relativity [duplicate]

Classical physics solves a two-particle Newtonian Universal Gravitation problem using: $F = -{G M m\over r^2 }.$ How is this problem solved using General Relativity? I am referring to the situations ...
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Can we “stir” space-time?

Depending on the energy-momentum density of a given region in space there is an intrinsic curvature to it. I can't help but feel like space-time is a like fluid, which begs the question whether it is ...
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Twin paradox in curved space time [duplicate]

In a flat space, where special relativity works, a travelling body can only return to the same point if we apply some kind of acceleration to the body. So twin paradox is not a paradox because a ...
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Spatial part of Robertson-Walker metric

The spatial part of the FRW metric can be written as $$d\Sigma^2=d\rho^2+f^2(\rho)(d\theta^2+{sin}^2\theta d\phi^2)$$ where $f(\rho)$ satisfies $$\frac{df}{d\rho}=\frac{f(2\rho)}{2f(\rho)}.$$ I am ...
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Directional derivatives involving tetrads turn into covariant derivatives?

In the tetrad formalism we define four vectors $e_{(a)}^i$ labelled by $a=1,2,3,4$ with components $i=0,1,2,3$ , such that they are related to the metric tensor by $$e_{(a)i}e^{(a)}_j=g_{ij}$$ while ...
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2answers
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Seems like the coordinate independent 1-form transforms like a scalar

I'm studying general relativity and and learning up on tensors through a lecture series. It says that $\omega_\mu$ represents a 1-form in the $x^\mu$ coordinate system. The coordinate independent 1-...
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Vectors transforming under change of coordinates

I was watching a lecture on tensors and the professor said that a defining feature of a vector $v$ is that it transforms under a coordinate transformation $x^{\mu} \rightarrow x^{\mu'}$ as $$v^{\mu'}...
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Notion of 'functional degrees of freedom' for the metric function in GR?

I have read through the numerous questions on 'degrees of freedom' in the metric tensor, and won't list them all here. However none of them address my question on 'functional' degrees of freedom in ...
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Why do accelerating bodies have an event horizon?

I read in a book named "Three Roads to Quantum Gravity" written by Lee Smolin that any accelerating body always have some hidden region of space-time from which light is never able to catch up with ...
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How do the properties of a Lie group (represented as a manifold) manifest in the metric tensor of that manifold?

I know this is a math question; however, physicists are more likely to be familiar with what I'm asking (also, I'm directly trying to utilize it in the context of general relativity). I may have ...
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Would a 5-dimensional black hole actually break laws of physics?

I discovered a paper by, Figueras, Kunesch, and Tunyasuvunakool, "End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture." A Cambridge University press release is here. The ...
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Rindler Metric and Minkowski metric

I am trying to understand why the Rindler Metric line-element and Minkowski metric line-element represent the same spacetime. Could someone help me understand that?
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A question regarding Leonard Susskind's ER=EPR lecture

https://youtu.be/OBPpRqxY8Uw?t=1315 Right at this instance of the video Susskind starts talking about how space is actually connected by entanglement. (You should watch the video for a accurate ...
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How does general relativity not work with quantum mechanics? [duplicate]

When people say general relativity doesn't work with quantum mechanics, which part are they actually talking about?
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Integrate isotropic coordinates [on hold]

When I take isotropic coordinates at the general metric for a static-spherically symmetric spacetime, finally you get the following integral: $$\dfrac{dr'^2}{r'^2}= \dfrac{dr^2}{r^2 (1-2M/r)}$$ i.e: ...
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Geodesics of anti-de Sitter space

It is said that (p. 9), given the anti-de Sitter space $\text{AdS}_2$, let's say in the static coordinates $$ds^2 = -(1 + x^2) dt^2 + \frac{1}{(1+x^2)} dx^2$$ Every timelike geodesic will cross the ...
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Given a black hole spacetime, how do we actualy find the event horizon?

As for a definition, there are quite precise ones for what an event horizon is. One can define it as the boundary of the causal past of future null infinity, i.e., $\mathcal{H}=\partial J^-(\mathscr{I}...
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How did inflation affect time-like space-time?

Alan Guth gave an overview of inflation in a series of videos for World Science U. The emphasis is on how inflation expanded a patch of space to the size of a marble, with no mention of how time-like ...
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Physical meaning of curvature in relativity [closed]

I understand space is not a rigid structure which actually bends (like a metal bar or rubber sheet) so "curvature" due to energy momentum pressure and stress (stress energy tensor) is?? This is were I ...
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Energy Equation of an ideal gas in expanding space-time

Short question: If the energy equation of an ideal plasma is written as follows: $\begin{equation} \frac{\mathrm{d}p}{\mathrm{d}t}=-\Gamma p\nabla\cdot v-\left(\Gamma-1\right)\left( \nabla\cdot q-\...
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How to get the four-velocity components from a given metric tensor?

I’m a little bit confused about how to get the four-velocity components from a given metric tensor (or line element). For instance, which are the components of the four-velocity in the Schwarzschild ...
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An non-orthodoxal example about electromagnetic energy-momentum tensor and EFE

This question is about the ementary notions about the physics of General Relativity. So, consider then the Einstein Field Equation (EFE): $$G_{\mu \nu} = \frac{8 \pi G}{c^{4}} T_{\mu \nu}$$ The ...
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Two meanings of acceleration in gravitational fields?

Question about General Relativity. Edit: I've gotten some really good input to help me better phrase my confusion. I think the heart of my problem is understanding the difference between geodesic ...
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What is the geometric interpretation of the Einstein tensor $R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R$

The Riemann curvature tensor $R_{\mu \nu \rho \sigma}$ has the geometric interpretation of giving how much parallel transport fails to close around tiny loops. The Ricci tensor $R_{\mu \nu}$ the ...
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What is a theory of gravity?

Let me introduce this question by noting that my training is in condensed matter physics, and my familiarity with gravity is superficial at best. Hence, this question may be somewhat naive. In ...
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The action of Einstein Maxwell system for arbitrary dimensions

The question is as mentioned in the title. To write the action for the Einstein-Maxwell system in arbitrary dimension. Is it possible just to add them (The Lagrangian for gravity and for ...
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Isotropy of the universe in different reference frames

Suppose that we put Bob and Alice into intergalactic space. If they look around they will see the light from distant galaxies shifted according to the Hubble law. More importantly, the light is (on ...
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Deriving Friedmann Equations without General Relativity

Can we derive the analytic Friedmann Equations without general relativity, starting from completely classical/nonrelativistic arguments? (If we consider sufficiently small volumes.)
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Divergenceless of energy momentum tensor for any metric $g_{\mu\nu}$

As suggested by @my2cts, from this post, I want to know if the divergenceless of energy-momentum energy tensor is valid for any metric $\eta_{\mu\nu}$ (i.e for example with $\eta_{\mu\nu}=g_{\mu\nu}$)?...
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Doubt about the vacua equations of General Relativity

I'm facing a quite annoying conceptual problem concerning the Einstein Field Equations (EFE) in so called "vacuum". This problem is both physical and mathematical. So, in a elementary point of view, ...
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Determinant of the metric tensor

After a change of coordinate system on flat space from $x\rightarrow y$, we have the metric tensor: $$g_{\mu \nu} = \frac{\partial y^{\alpha}}{\partial x^{\mu}} \frac{\partial y^{\beta}}{\partial x^{\...
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Way of splitting spacetimes into space and time

On several occasions, we would like to separate the components of the metric into three sets ($g_{00}$,$g_{0\alpha}$,$g_{\alpha \beta}$). Please refer to exercise $4.2$ of "Gravitation, Foundations ...
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Does the total volume of space change in a n-body problem?

Say you have a few massive objects like planets which bend and warp space-time in an otherwise empty space. They move about in a region of size R, perhaps like a solar system. Then you calculated the ...
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Riemann curvature in orthonormal frame and Lorentz transformations

I have problem with understading how Riemann tensor in orthonormal frame transforms using Lorentz transformation of frames. I was reading Morris Thorne paper from 1988 (American Journal of Physics 56, ...
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Maxwell Equations in Friedman-Robertson-Walker metric

The Maxwell equations are relativistic. But what happens to them in an expanding space time? I assume that only the charge density $\rho$ is affected, i.e. only Gauss's law gets modified. Am I right ...
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Timehole - Black hole physics [closed]

If someone could shed some light so that I can think straight again that would be appreciated.. Anywho, since watching a video on what the universe may look like in trillions of years (each atom ...
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Difficult coordinate transformation

I am trying to introduce a tortoise coordinate for a modified Schwarzschild metric $$\mathrm{d}s^2=\left(1-\frac{2M\mathop{}\!\mathrm{erf}(r)}{r}\right) \mathrm{d}t^2 + \left(1-\frac{2M\mathop{}\!\...