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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Linearized theory and gravitational waves
I've been reading the chapter about gravitational radiation of Schutz's book.
In one of the sections, he begins with the linearized Einstein's equations and tries to find an intuitive solution:
$$(-\...
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Is the gravitational tidal force equivalent to expanding space?
If you fall towards a black hole, the particles in front and the back of you, in the direction of the center, are accelerating away from you. So, seen from a freely frame, can we say that space is ...
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How to calculate Proper Distance as an arc length in Schwarzschild metric?
I am trying to determine the method to calculate proper distance with constant time and radius in Schwarzschild Geometry. With only $\theta$ and $\phi$ being variable. I think it involves integrating ...
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Can Black hole eat white hole or white hole eat black hole? [duplicate]
No light can enter black holes, but is it possible for a white hole to enter a black hole? Or vice versa? Could there be black holes inside the white holes? Or were there black holes inside them that ...
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The Derivation of the Schwarzschild Solution
I went to this site to find the solution. However, I have a few questions about where these equations come from.
In the category of Assumptions and Notations, what equation gives you $\partial_tg_{\...
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How to simplify the process of calculating spacetime geodesics?
I want to study the movement of a particle along geodesics in an expanding universe with metric (FRW metric)
$$
ds^2 = -dt^2 + a^2(t) \left( \dfrac{1}{1-kr}dr^2 + r^2 d\theta^2 + r^2 \sin^2\theta d\...
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How do I calculate the functional derivative of the EM action on the curved spacetime with respect to the metric?
I am having trouble with computing the functional derivative with respect to the metric of the EM on a curved spacetime:
\begin{equation}
S:=\frac{1}{16\pi^2 G}\int R \sqrt{-g}\text{ }d^4x-\frac{1}{4}\...
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Smooth vs analytic spacetimes
Recently in more technical settings (I was learning algebraic QFT), I encountered the term "real analytic" manifolds (Lorentzian manifolds, to be precise). This is in contrast to smooth ...
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Cosmological expansion around ropes between galaxies
The FLRW cosmology is a fair approximation of cosmological expansion for space between galaxies and clusters, however within galaxies themselves, is known to not hold, and in fact observational ...
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How does it make sense for the universe to have started from a big bang?
It has been said that the Big Bang started from a singularity. Think about a balloon radially growing over time. Fix a time $t_0, t_1 > 0$, and let $M_0, M_1$ be two balloons at time $t_0, t_1$ ...
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Linear Momentum in General Relativity
My question is, does a particle moving in a straight line at constant velocity through empty space create "frame dragging" that would tend to entrain other bodies in the direction of its ...
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Geodesics of a rotating sphere
I know when we live on a rotating sphere we feel virtual forces. By these forces how can we define our geodesics? l think these geodesics are different with the geodesics of a non-rotating sphere.
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Will a light come back within finite years?
In this answer Javier said
Imagine the universe was the inside of a ball. We're 3D now, so no one is hiding any dimensions. This ball has a border, except it's not really a border. You should think ...
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If an object is accelerated fast enough, will it become a black hole? [duplicate]
I know that if an object is accelerated, its relativistic mass increases. Does this mean that if it is accelerated fast enough, it will become so massive that it becomes a black hole?
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What are the three bright spots in the Sagittarius A black hole picture? [duplicate]
Today the first picture of the Sagittarius A black hole was released. Although somewhat similar to the first picture of the M87 black hole released three years ago, to my eye there's a notable ...
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Does the stress energy tensor scale with the metric tensor?
Question
I had some thoughts from a previous question of mine.
If I have a metric $g^{\mu \nu}$
$$g^{\mu \nu} \to \lambda g^{\mu \nu}$$
Then does it automatically follow for the stress energy tensor $...
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Why are there three bright spots in the first picture of Sagittarius A*?
Why are there 3 distinct bright spots? The picture of the black hole in M87 had half bright and half dark, which I believe is a result of the different relative velocities of particles orbiting it, (...
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Would an accelerated-time space region deflect projectiles?
Suppose a spherical region in space in which time goes faster.
Would projectiles shot at it be deflected away, as light is deflected by a material with a lower refractive index?
Edit: This would also ...
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Could dark matter be just a gravitational effect of dark energy?
I'm wondering if we just looking at the two sides of the same coin and if there is actually a correlation of DM with DE?
Is it possible that DM just to be a gravitational effect (or an effect that ...
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Conserved charge at null infinity associated with Large gauge transformation
I am reading Strominger's lecture notes "Lectures on the infrared structure of gravity and gauge theory" (https://arxiv.org/abs/1703.05448). At some point, following (I guess) the authors of ...
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Why aren't all photons black holes?
According to Special Relativity, there is no preferred inertial reference frame. And shifting reference frames can cause blue shifting or red shifting of photons.
And according to General Relativity, ...
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A synchronous clock problem in a rigid frame with constant proper acceleration
I am a beginner of general relativity. I read and follow the notation in Andrew Steane's book, Relativity Made Relatively Easy, chap 9.2. Suppose there is an rigid accelerating frame with constant ...
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Calculating divergence and flux of geodesic word lines
Given a family of neighbouring geodesic word lines, is there a way of calculating properties such as their divergence or flux? maybe by converting the tangent vectors of the world lines to a vector ...
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Mutual gravitational acceleration (or deflection) of light beams as a function of the angle between them
Given Einstein's famous equivalence between energy and mass, $E=mc^2$, a light beam with power, $P$, has an energy per unit length of $P/c$ and an equivalent mass per unit length of $P/c^3$. A short ...
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Generalizing Fermi-Walker Derivative/Transport to General Vector Bundles
The usual definition of the Fermi derivative (eg as given in Hawking and Ellis) is to consider a Lorentzian manifold $(M,g)$ and a unit timelike curve $\gamma$, a smooth vector field $X$ along $\gamma$...
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In and out states of scattering in Asymptotically flat spacetimes
I am reading a paper called "New symmetries of massless QED", written by Temple He, Prahar Mitra, Achilleas P. Porfyriadis and Andrew Strominger (https://arxiv.org/abs/1407.3789). At some ...
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Why does a null entropy variation along a closed timelike curve imply a reversible process?
Carlo Rovelli in one of his articles from 2019 (reference: https://arxiv.org/abs/1912.04702) argues that time travel into the past are thermodynamically impossible:
For instance, if we want to travel ...
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Riemann curvature tensor in an inertial frame
My understanding is that the mathematical definition of an inertial frame at $x_0$ is a choice of coordinates s.t:
$g_{\mu\nu}(x_0) = \eta_{\mu\nu}(x_0)$
$\partial_\rho g_{\mu\nu}(x_0) = 0$
I've ...
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Is the Planck force a truly "Planck unit"?
The Planck force appears to be defined as the ratio of the Planck energy to the Planck distance, $ F_P = E_P/l_P $ that can be rewritten as $$ F_P = \frac{ E_P }{ l_P} = \frac{ c^4 }{ G }. $$
Isn't it ...
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Brief electron-positron pair creation annihilation and light deflection by gravity
According to QFT there exists a non-vanishing probability amplitude for the following process:
a photon very briefly turns into an electron-positron pair
which then annihilate each other almost ...
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Calculate the luminosity distance in terms of redshift and the scale factor
Suppose you are in a spatially flat universe with a single parameter of the equation of state, $w$. Now for $w\neq -\frac{1}{3}$ calculate the luminosity distance in terms of redshift ($z$) and $w$.
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Carroll's derivation of Hawking radiation
In Carroll's Spacetime and Geometry: An Introduction to General Relativity, in his derivation of Hawking radiation Carroll makes the following statement:
"as observed over length and timescales ...
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Constraining the metric on the boundary of space-time to get rid of unwanted equation of motion
I've posted this question on maths.stackexchange discussing the action I'm working with, which is (in Dirichlet boundary conditions) just the effective action of a minimally coupled free massive ...
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Can point masses following geodesics and orbiting one another emit gravitational radiation?
I am a bit confused about this situation: according to general relativity, when two masses orbit one another, they emit graviational waves, which carry away certain energy. For example, check out ...
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Are tensors constructed such that one forms "act" on some complex vector field?
I have some confusion understanding the motivation in constructing tensors (or tensor fields). On a differentiable manifold $\mathcal{M}$ consider a vector field $X$. At any point $p\in \mathcal{M}$, ...
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How is the gravitoelectromagnetism approximation of GR valid if it seems to yield unstable solutions?
In the gravitoelectromagnetism approximation of GR, we have equations analogous to Maxwell's equations with some sign changes. As pointed out in another post of mine, this leads to unstable run-away ...
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Does this special relativistic identity hold in General Relativity?
So I came across the following identity in the fascinating book: "Beyond the Einstein Addition Law and it's Gyroscopic Thomas Precession":
$$\gamma_{u \oplus v} = \gamma_u \gamma_v\left(1 + \...
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How to calculate the Kretschmann scalar in 3+1 decomposition?
Does anyone know a source for calculating the Kretschmann scalar and/or 4D Riemann tensor using the variables of the 3+1 decomposition?
I need to monitor a curvature invariant and calculating it ...
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What does it exactly mean when we say that a photon or light is "frozen" at the event horizon?
Objects on this site are said to "freeze" at the event horizon, but what about photons themselves?
I have read this question:
At the event horizon $v_{eff} = 0$ and the light beam is frozen ...
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Schwarzschild-deSitter horizon singularity
The Schwarzschild-deSitter spacetime in Euclidean signature is given by:
$$
ds_{E}^{2}=\left(1-\frac{2M}{r}-\frac{H^{2}r^{2}}{3}\right)d\tau^{2}+\frac{dr^{2}}{\left(1-\frac{2M}{r}-\frac{H^{2}r^{2}}{3}\...
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How is it that we are still able to talk about the speeds of other galaxies, distances and times across the universe, etc despite GR?
Science articles often say that Andromeda galaxy is approaching us with speeds such and such. Sometimes we say that the universe is expanding away faster than light. Sometimes we talk about things ...
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Where does gravity come from?
First, in my childhood, I learned that gravity is a force. Later, I learned that gravity is a property of spacetime. If gravity is a property of spacetime, then why is it one of the fundamental forces....
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How does general relativity resolve the fact that energy is not positive definite in Newtonian gravity?
In Newtonian gravity, the energy of the gravitational field $\vec{g}$ is
$$ U = -\frac{1}{8\pi G}\int |\vec{g}|^{2} d^{3}x $$
(assuming we don't have any point masses that lead to singularities and ...
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What is the evidence that gravitational fields don't sum up as a superposition?
Einstein's field equations are non-linear. Gravity gravitates (self-interacts). It's very complicated to solve Einstein's field equations for more than one central object. That are keystones in ...
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Self-coupling of gravity and gravitation escaping a black hole - contradiction?
The field equations are non-linear, that can be interpreted as gravity is coupling with itself, see for example here:
Non-linearity and self-coupling of gravity
I'm trying to understand what that ...
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Help in understanding how general relativity describes space-time near black hole poles that emit astrophysical jets
I am aware that General relativity does not explicitly deal with 'expanding' or growing and due to that reason 'cosmologically pressurised' aether (proposed by the 'Theory of a river flow' but that ...
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Trying to derive newtonian potential for Schwarzschild interior metric [closed]
I am using the book "A first course in general relativity" by Bernard Schutz. On page 267 he derives equation 10.54 but leaves out some steps that I am trying to do myself. The following is ...
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Variational operator confusion
Let $L=L(X, \dot X)$ such that the first variation of $L$ is given by $$\delta L=\frac{\partial L}{\partial X}\delta X+\frac{\partial L}{\partial \dot X}\delta \dot X.\tag{1}$$ This is pretty standard ...
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Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter?
Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter?
If so, can we extend Einstein field equations globally relating global spacetime curvature to ...
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Physical significance of metric compatibility
When we try to construct a covariant derivative, we impose several conditions on it so that the resulting derivative is unique. However, I can't make sense of the condition of metric compatibility. I ...
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