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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Schwarzschild Radius of a Galaxy

If an ultra compact/dense Galaxy has a Schwarzschild radius same as it is own radius, how can it be observed from the outside of the Galaxy?
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What are the pros and cons of Einstein-Cartan Theory?

As an alternative to General Relativity, i hear that it can avoid the initial big bang singularity as well as the singularities in black holes, so why does it appear to be talked about so little? If ...
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Greatest relativistc mass possible for a single photon

I have been told that photons can not be blue shifted to the point where they become black holes, although a photon with a Planck scale wavelength would also have a relativistic mass equal to a black ...
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What's the covariant derivative of a normalized, timelike Killing vector?

I'm reading The large scale structure of spacetime and in page 72 the author says: A static metric admits a timelike killing vector $K$. We define the timelike unit vector $V$ as $V=K/f$, where $f^...
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Any theory/author using the white hole model to explain the birth of the universe?

The maximally extended Schwarzschild solution (Kruskal diagram) envisages a white hole, which is the time-reverse of a black hole, i.e. a part of spacetime from which things can escape to us, while we ...
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How to get the Bertotti-Robinson metric into its conformally flat version?

The Bertotti-Robinson metric is a very nice exact solution to the Einstein-Maxwell field equations in vacuum. It is usually stated into these equivalent versions (where $r = \sqrt{x^2 + y^2}$ and $\...
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Two particles at different points on a curved manifold

Stupid question, but why two particles at different points on a curved manifold do not have any well-defined notion of relative velocity? For instance n cosmology the light from distant galaxies is ...
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Relativistic constant acceleration in the framework of general relativity

Regarding the constant acceleration of a spacecraft towards relativistic velocities, the general equations are found at the following link: Baez However, if the distance covered is in excess of 1 ...
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A Second Geodesic Equation?

I have a question about the geodesic equations. I understand the following formulation of it: $$\frac{d p^\mu}{d\tau} = - \Gamma^j_{v\mu}p^vp^\mu.$$ However, I was reading https://arxiv.org/abs/1305....
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Detectability of gravitational waves emitted by a free-falling object, by different observers

Does an object falling radially in a gravitational field of a planet emit gravitational waves as seen by an observer on the surface of the planet? What about an observer falling along with the object?...
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Trace-reversed stress-energy tensor notation [on hold]

Let: $g_{\mu\nu}$ be the spacetime metric $R_{\mu\nu}$ be the Ricci curvature tensor $R = g^{\mu\nu}R_{\mu\nu}$ be the scalar curvature $G_{\mu\nu}=R_{\mu\nu}-\frac12 Rg_{\mu\nu}$ be the Einstein ...
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How to find the terms of Post-Newtonian approximation

I am studying the Damour paper on the Post-Minkowskian approximation to the 2 bodies problem in General Relativity (paper) but can't really understand the explanation of the previous state of the art, ...
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Inside the singuarity [on hold]

This thread may be off-stream physics but it is related to a very interesting subject . What happens to the centre of a black hole ? Do quantum effects become dominant or is GR totally correct? ...
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A few questions about white holes

White holes are seen in the maximally extended Schwarzschild solution, they are a region from the past that appear in the theory of eternal black holes, where the singularity exists in both infinite ...
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Is there a Shapiro time delay to a signal sent to the outer solar sytem and back?

The Shapiro time delay to a light signal has two equal halves, according to Clifford Will, the space part and the time part. The time part is just the slowing effect of gravitational time dilation. ...
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Why can't gravity force an object past the speed of light? [duplicate]

I hope this question is not a duplicate (it doesn't seem to be) and that it is appropriate for this site. If we had a universe with only two bodies. One is ultra massive, and the other is very small. ...
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Has the speed of light ever been measured in vacuum?

According to: https://en.wikipedia.org/wiki/Cosmic_microwave_background the CMB (Cosmic Microwave Background) "is faint cosmic background radiation filling all space" Also, https://en.wikipedia.org/...
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Complex Scalar Fields and Killing Vectors

In a stationary and axisymmetric spacetime, there are two Killing vectors, say $\zeta^\mu$ and $\xi^\mu$, one timelike and one space like. I understand that for a real scalar field, $\phi$, that ...
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Coordinate independence in spacetime

As far as I know, the $n$ coordinates $(x_1, x_2, ..., x_n)$ chosen to describe an $n-$manifold have to be mutually independent $\to$ the mutual derivatives must equal $0$ (for example, $\frac{dx_1}{...
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Variation of the metric w.r.t. the metric in derivation of stress tensor

Consider massless free scalar theory $$S = \int d^4x \sqrt{-g}L = \int d^4x \sqrt{-g} \;g^{cd}\nabla_c\phi \nabla_d \phi.\tag{1}$$ To compute the Hilbert stress-energy tensor we require $\sim\delta S/\...
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What is a layman explanation for why the wavelength of light increases when space itself expands?

I understand that the universe is generally agreed to be expanding based on observations. What I have read is that space itself is expanding. My question is why does this expansion of space affect the ...
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1answer
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Is there a cosmological constant $\Lambda$ in 2D?

It is well known that the Einstein tensor is trivially 0 in any two dimensions spacetime: \begin{equation}\tag{1} G_{\mu \nu}^{(2)} \equiv 0. \end{equation} Thus, it is not possible to formulate the ...
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Can a person from different universe which has its “own different laws of nature”, can go into our past in our Universe? [closed]

Suppose There is a Universe, which has different laws of nature than ours galaxy and they have much greater speed of light than $3* 10^8 $ m/s ,so some person from their universe visits our universe ...
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Manev potencial and some problems with it [closed]

Given the Manev potential by the equation below $$\ V_M(r) = - \frac{-mMG}{r} \left(1 + \frac{\gamma MG}{c^2r}\right) $$ in which: M is the Sun's mass; m is the planet's mass; G is Newton's ...
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Transformation of four-vectors and basis vectors

I was taught that vectors are one rank tensors, so under diffeomorphism they do not change (their components do change but not them as tensors) they are contravariant, i.e. \begin{equation} A = A^{\mu}...
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Wedge product, tensor product, and Levi-Civita tensor/symbol

Source: Pages 89 and 90 of Sean Carroll's Spacetime and Geometry Quite a confusion in two steps of this quantity: $$ \begin{eqnarray} \sqrt{|g|}d^n x &=& \sqrt{|g|}dx^0 \land ... \land dx^{...
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How to find a coordinates transformation on $A\,\mathrm dS_2$?

I have the following 2D metrics (describing the $AdS_2$ spacetime), which are supposed to be the same in different coordinates: \begin{align} \mathrm ds^2 &= \mathrm dt^2 - \sin^2{\!\omega t} \, \...
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Black hole in timespace: point or “trench”? [duplicate]

I wonder what is the nature of a black hole as set of points of manifold. A single point (with infinite curvature) or a "trench" ? I thought that it is a "point", but since black holes can collide and ...
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Non-linear Perturbations of Minkowski Spacetime

I am reading some of the following paper on the bounded $L^2$ conjecture in general relativity where it mentions non-linear perturbations of the Minkowski metric in the context of quasilinear wave ...
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Can I use the expansion of the universe to create or destroy energy?

Imagine I have a setup like this: (The objects are not attached to each other. The red objects are much heaver than the black one, and the setup is balanced.) This setup has a non-zero ...
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Why does FTL not leave behind a motion blur? [closed]

I once thought anything traveling faster than light would leave behind a motion blur that on one end recedes at the speed of light and at the other increases at the velocity of the object. If an ...
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1answer
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Define event horizon using only the notions of events and causality

Does this work? Consider a set $B$ of events which satisfies If $x$ belongs to $B$ and $x$ causes $y$ then $y$ belongs to $B$. The event horizon of $B$ is the set of events that are not in $B$ but ...
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Interpretation problem with Melvin and Bertotti-Robinson magnetic universes

I'm having an interpretation problem with two models of magnetic universes in General Relativity. Firstly, consider the Melvin universe described by the following static metric: \begin{equation}\tag{...
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Is it acceptable to add a scalar to the lagrangian of general relativity?

Starting from $$ L=\sqrt{g_{\mu\nu} \frac{\partial X^\nu}{\partial t} \frac{\partial X^\mu}{\partial t }} $$ One can rewrite it as $L\to L^2/2$ $$ \frac{L^2}{2}=\frac{1}{2}g_{\mu\nu} \frac{\partial ...
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Does general relativity predict that the gravitational field of a black hole would be uniform about its center of mass?

Black holes are typically represented by extreme distortions of space, where space is so bent, that it reaches a single point (i.e., the singularity). Further, they are almost always depicted as ...
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The equation of motion for a scalar field in curved spacetime in terms of the covariant derivative

The equation of motion for a scalar field in curved spacetime $$\frac{\partial\mathcal{L}}{\partial\phi}=\frac{1}{\sqrt{-g}}\partial_{\mu}\left[\sqrt{-g}\frac{\partial\mathcal{L}}{\partial\left(\...
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Can I get a single matrix from Einstein’s summation

A simple question guys, I have this equation $ g^{m \bar{n}} g^{r\bar{p}} \partial_t {g}_{m r} \partial_t {g}_{\bar{n}\bar{p}} = X_{i\bar{j}}~ \partial_t{f}^i (t) ~ \partial_t{f}^\bar{j} (t) $ ...
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Does $\mathcal{M} = AdS_2 \otimes S_2$ makes any sense as a manifold?

I'm not a topologist or a group theorist and I need a clarification about some notations. Consider the Bertotti-Robinson metric in General Relativity (relativity students should study this metric, by ...
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Marginal Surfaces in Spacetimes

Is there some result on existence of marginal surfaces in spacetime 4-manifolds? Am I right in saying that a marginal surface (like a trapped surface) is a compact spacelike 2-surface by definition,...
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When looking for a black hole, will we always find a collapsing star instead?

I know that from the point of view of an outside observer, the collapse of a star into a black hole never finishes, i.e. any observer will always see a (red-shifted) version of the star before its ...
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Is there an experiment showing that the warping of space affects the shape of an electrostatic field? [duplicate]

General relativity assumes that space itself is warped by gravity, which is what gives rise to the shapes of the paths followed by objects subject to a gravitational field. If space itself truly ...
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On the Boundary term in $f(R,T)$ Gravity

In standard $f(R)$ gravity we consider the Lagrangian of the form $L=\frac{1}{16\pi G}f(R)\epsilon$, where $\epsilon$ is the spacetime volume form and similarly, we consider the boundary term to be of ...
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Perturbations of a Background Spacetime

I am reading some lecture notes on general relativity, where the author talks about perturbation theory applied to GR. In the case of a weak gravitational field, one perturb about the Minkowski ...
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Does the age of the universe depend on the way it is defined?

I was reading some earlier posts on this question in stack exchange. These posts give me the impression that the age of the universe is defined in a certain way following prescriptions such as that: ...
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Is the mass needed to create a black hole greater if the black hole is moving? [duplicate]

So my argument goes like this: say we have an object that is nearly at the density required for a black hole. Then we Lorentz boost into a new frame, the object is Lorentz contracted and therefore ...
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How can we tell if the Earth is spinning without any external references? [duplicate]

The rotation of the Earth about its axis makes it bulge at the equator and contract at the poles due to the centrifugal forces. How do we know, without any external references, that the Earth is ...
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Outer-Minimizing Property in Majumdar-Papapetrou Slice

In the canonical space slice of the Schwarzchild spacetime, which is the manifold $\mathbb{R}\times S^2$ with the metric $ds^2=\left( 1 -\frac{2m}{r} \right)dr^2 + r^2 d\omega^2$ it is well known ...
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Can an observer perceive a single source of light as multiple sources because of curved spacetime?

Is it possible that some of the stars and galaxies we observe here on Earth are actually replicates of other stars and galaxies we are observing from different angles because of curved spacetime? Let'...
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Dirac matrices for generalized metric tensors

The Dirac matrices are defined by the relations $$\left [\gamma^{i},\gamma^{j}\right]_{+}=2\eta^{i,j}\mathbb{1}$$ where $[\cdot,\cdot]_{+}$ is the anti-commutator. What happens if I replace $\eta^{i,...
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Are there any experimental data about potential time dilation caused by cyclical movement of heavy objects?

I am dealing with a completely fabricated scenarios (while trying to write a sci-fi book), so my thougts are completely hyphotetical. But I would like to ask you to help me find out if following ...