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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Can I form a scalar with coordinates in general relativity?

There is no position vector in general relativity. I was wondering whether a quantity like $$k_\mu x^\mu$$ where $k_\mu$ are covariant vector components is to be treated like a scalar i.e. invariant ...
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David Tong's definition passive transformation of the fields looks wrong

David Tong's definition of active transformation is clear. Under active transformation coordinates (basis vectors) are not changed but rather the field is. I denote the old and new fields as $\phi$ ...
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Why is “Gravity as a result of space-time curvature” not accepted as a fact? [duplicate]

Now that gravitational waves are confirmed. Not to mention the other numerous experimental verifications. Why do we still need an elusive graviton? Isn't there not enough evidence that the space-time ...
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What is the connection between topology and physics? [closed]

I'm a physics undergrad student, but this year I had the chance to take general topology course. It is a wonderful topic, and I have read it has some applications in physics.
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Why does the flow of time slow down as the space-time curvature gets deeper?

According to General Relativity and its experimental tests, a clock far above Earth ticks faster than it does on the surface of Earth. Because near the surface of the Earth space-time curvature is ...
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Einstein summation and square roots

It has occurred to me I don't know if there is a general rule about this or not. If I have an expression like: $$\int \sqrt{g_{ij}\frac{dx^i}{dt}\frac{dx^j}{dt}} dt$$ I take the summation inside the ...
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Metric field equations for the Jordan-Brans-Dicke action

Considering the Jordan-Brans-Dicke action: $$S=\int d^4x\sqrt{-g}\left(\phi R+\frac\omega\phi(\partial\phi)^2+\mathfrak{L_{m}}(\psi)\right).$$ I was trying to get the metric field equations by varying ...
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Zee General Relativity Transforming polar coordinates to Riemann normal coordinates

This is from Zee's book on General Relativity. This is from Book 1, Part 1.6, on he bottom of page 89 as a "fun exercise". Using $$g_{\mu\nu}=\delta_{\mu\nu}+B_{\mu\nu,\lambda\sigma}x^\...
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If gravitational field is not real, then am I gaining energy?

I don’t know much about General Theory Of Relativity but I have heard that it does not consider gravitational fields like Newtonian Mechanics. If an object were to be free falling, then according to ...
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Confusion in Wald's GR book: observers correspond to orthonormal basis

Book: General Relativity by Robert Wald (pgs: 342-343) He starts out by suggesting that observers in general relativity correspond to orthonormal basis fields on the manifold, which I am OK with. ...
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Understanding the four-dimensional volume form in Action of Lagrangian

Into the following part below, I don't understand what is precisely a "four-dimensional volume form" implied in the integral below: For comparison, the ...
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Demonstration of the Brans-Dicke's Lagrangian

The Lagrangian in general relativity is written in the following form: $$ \begin {aligned} \mathcal {L} & = \frac {1} {2} g ^ {\mu \nu} \nabla \mu \phi \nabla \nu \phi-V (\phi) \\ & = R + \...
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General treatment of connections and covariant derivatives

Hi have been following an introductory course on quantum gravity and we are covering the basics of free quantum field theory in curved spaces. I have been introduced to how spin connections play a ...
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Does the energy density of space create cause gravitational attraction beyond what would be computed from an object's mass alone?

I am starting from the assumption that the gravitational warping of spacetime increases its volume, so a spherical region of space with a fixed surface area would be able to fit a larger number of ...
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Christoffel symbols in exact plane waves

In the book "A first course of General Relativity" by Schutz I am stuck in trying to calculate Christoffel's symbols for an exact plane wave. I have the metric: $$ds^2 = -dudv+f^2(u)dx^2+g^2(...
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Determinant metric tensor

I do not understand the relation between the determinant of the metric tensor $g$ and the non-tensorial symbol $\tilde{\epsilon}_{\mu_{0}..\mu_{n}}$. This is explained in Carrol's book as followed: \...
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Why can’t gravitons distinguish gravity and inertial acceleration?

If gravitons mediate the gravitational force, couldn’t the detection of gravitons by an observer be used to distinguish whether they are experiencing gravitational acceleration vs. inertial ...
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Nilpotency of BRST operator in gravity

I am going through the BRST quantisation in Perturbative quantum gravity and looked at the papers of Nishijima and Ojima. I am confused about the closure of the BRST operator; I.e $s^2=0$, ...
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Book Recommendation on Math needed for General Relativity

Today, I had to do an exercise that talked about conformal geometry and after spending a ridiculous amount time searching for it in General Relativity books I couldn't find it. In books like Ray D'...
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Derivative of the Metric Tensor With Respect to a Scalar Field

In Sean Caroll's Spacetime and Geometry Textbook, at page 183 (discussing scalar-tensor theories) Carroll defines a conformal metric by performing a conformal transformation as: $\tilde{g}_{\mu\nu} = ...
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Doubt in tensor calculus in General Relativity

I am stuck in the derivation of $G$ (Einstein tensor) in the condition of weak field ($h$ small) where $g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}$ and $h^{\alpha\beta}=\bar{h}^{\alpha\beta}-\...
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Definition of spacetime in GR

In all the references/textbooks that I have looked at, the precise definition of spacetime is never really clear. By gathering the hypothesis that we need to make, I get the following definition: $$\...
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Spherical collapsus according to a running observer [closed]

Imagine that a spherically symmetric body goes through a gravitational collapsus. In $ t_1 $ event horizon builds up instantly. Then say that somebody runs next to the collapsing body with ...
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Conceptual problem with general relativity

According to Einstein, mass curves spacetime and objects in the nearby field tends to travel in the shortest possible path to reach their heavier counterparts. My question is was not Newton's ...
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1answer
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Locally Flat Understanding

I wanted to make sure that I was definitely understanding the proof of locally flat correctly. I can't see to find a similar proof to the one in the book, so I'm not super sure if my understanding/...
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Is spacetime curvature and the shape of the planet is the same?

Let's say you're telling the story about two people starting walking toward the north pole from two different points (one from LA the other from NY), they going to walk straight line, but nevertheless ...
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How can Earth accelerate toward US and China with no expanding? [duplicate]

In this video it's explained that there is no gravity force, it's all acceleration: Earth moving toward us, but how that's possible without expanding (toward people standing on the opposite sites of ...
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What does a rotating universe look like?

If everything in the universe were revolving around an axis, how would that affect space-time? In my mind it would be no different from a normal universe since it would look normal in a comoving frame,...
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Euler's equation from energy-momentum tensor conservation

Given the energy-momentum tensor for a perfect fluid: $$T^{\mu\nu}=(\rho+p)u^{\mu}u^{\nu}+pg^{\mu\nu}\space\space\space\space\space(1)$$ I was trying to obtain Euler´s equation: $$ (\rho+p)u_{\lambda;\...
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We can't use numerical simulation for Hawking radiation backreaction, right?

In the last passage of 1975 paper Hawking tells that we can't use a local stress-energy tensor to tackle the backreaction of radiation since creation of particles is a non-local and global process ...
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Doubt on Newman-Janis algorithm for a traversable Wormhole

Recently in a paper $[1]$ the researchers presented a rotating traversable wormhole solution using the famous Newman-Janis Algorithm $[2]$. But something is anoying me. In $[1]$ they presented the ...
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If an event horizon never forms for an outside observer, then what do (or don't) we see in the middle area on this real image of an actual black hole?

There are a lot of questions about the m87 image on this site, non of them actually answer my question. I have read this question: Does an expanding event horizon "swallow" nearby objects? ...
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Physical interpretation of the nil ADM mass of gravitational waves

The ADM mass is defined for any asymptotic flat spacetime. Using cartesian coordinates: \begin{equation}\tag{1} E_{\text{ADM}} = -\: \frac{1}{16 \pi G} \, \lim_{r \, \rightarrow \, \infty}\oint_{\...
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What are the local Lorentz transformations in general relativity?

What is the exact form of local Lorentz transformations (from the point of view of the metric) in a curved spacetime background like in general relativity? It should deviate substantially from ...
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Radially-dependent stress-energy-tensor(?)

When we solve the Einstein Field Equations $G_{\mu\nu} = 8\pi T_{\mu\nu}$ one way of doing it is by specifying a symmetry (and thus a general form of the metric) and then specifying the stress-energy-...
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Covariant derivatives in a rank 2 tensor

I was trying to prove that for any second order tensor: $$A^{\mu\nu}_{;\mu\nu}=A^{\mu\nu}_{;\nu\mu}$$ considering the torsion free property and locally flat coordinates. Considering the point where ...
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Euclidean anti-de Sitter space embedding

Let us take $\mathbb{R^{d+2}}$ with the cartesian coordinates $(X_0,\dots,X_{d+1})$ and the following metric : \begin{equation}\label{equ1} ds^2 = -dX^2_0-dX^2_{d+1}+\sum^d_{i=1}dX^2_i. \end{equation} ...
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Why does an oscillating mass does not produce gravitational waves (in contrast with an oscillating electric charge)? [duplicate]

I would like to gain insight about this question. I have read it is related with the conservation of momentum, but cannot really differentiate it from the oscillating charge. The monopole radiation ...
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Does a stationary charge in a gravitational field radiate?

According to the equivalence principle, a freely falling observer constitutes an inertial frame. Thus, locally, Maxwell's equations apply in their usual form. According to these equations, an ...
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Is there a GR solution for the geocentric system?

It is possible to get the Schwartzschild metric assuming spherical symmetry, vacuum solution and Minkowski spacetime when $r \to \infty$. Is it possible an analytic solution for a geocentric system? I ...
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How is the fabric of space-time curved? It bends due to energy or mass, but what causes bending? [duplicate]

When we experiment with General Relativity on Earth, a tissue bends according to the experiment due to the placement of a mass, but of course there is a gravitational pull that causes bending. If we ...
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1answer
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Lagrangian in reduced Horndeski Theory for i=2

I am trying to understand the calculations of the latest Charles Dalang's paper "Scalar and Tensor Gravitational Waves", arXiv:2009.11827. Since I just learned basic general relativity, I ...
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Field equations involving a field potential term

We are given an action of the form: $$S=\int d^4x\sqrt{-g}\left(-\frac14F_{\mu\nu}F^{\mu\nu}+V(B_{\sigma}B^{\sigma}) +R\lambda B_{\mu}B^{\mu}\right).$$ where $R$ is the curvature scalar, $\lambda$ is ...
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Metric field equations

We have an action of the form: $$S=\int d^4x\sqrt{-g}\left(\frac{R}{2\kappa^2}+\frac14F_{\mu\nu}F^{\mu\nu}+\frac12m^2A_{\mu}A^{\mu}\right).$$ Here $R$ is the curvature scalar, $A_{\mu}$ is a vector ...
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$R=0$ solution in field equations

I am dealing with some General Relativity extensions and I am not sure about my knowledge in basic GR since I am having some weird troubles with what I think are basic concepts. As far as I know, if ...
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Conditions on one forms [closed]

I am trying to solve exercise 8.3 from Lightman's problem book, but I don't know where to start to get a sufficient and necessary condition on a field of one forms $\tilde\sigma$ for there to exist a ...
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Describing spacetime with qubits

Susskind in one of his lectures at PiTP 2018 on Complexity and Gravity talks about describing black holes as a qubit system, comprising qubits of the order of the entropy of the black hole. This is ...
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Apparent horizon buildup in a BH merger

I just read some articles about binary BH merger simulation. These state that at a certain instant a common apparent horizon(or MOTS) appears, surrounding the two BHs. This instant is called the ...
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Is it possible to make a tiny approximation in the equations of General Relativity so that they collapse to Newton's law of gravity? [duplicate]

GR and Newton give almost exactly the same result for the orbits of planets and the acceleration of falling bodies. Is it an incredible coincidence, or does GR have some tiny term (e.g., ict) that ...
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Free-falling object: When should we consider General Relativity?

My question is related to a statement: If a pendulum is experiencing free fall, then it will not oscillate. The statement is true in the sense that its acceleration is (approaching to) zero, then ...

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