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 we add two singularities and make a single singularity? [duplicate]

My question is if we have two black hole and they will merge into each other, then where will be the singularity?
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0answers
35 views

Clarification of Type D space-time

I've asked this question on MathOverflow but received no feedback, so I thought I'd try better luck here. I've read the following formulation of the Goldberg-Sachs theorem in Chandrasekhar's ...
2
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1answer
79 views

Infinite dimensional manifolds in general relativity [closed]

In GR the concept of a manifold is very useful. However, all of these manifolds are of finite dimension. Is it possible to define a manifold with infinite dimension (ie much like Hilbert space in QM) ...
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3answers
127 views

GR time dilation cares only about local curvature, right?

Regarding this remark on Worldbuilding SE and the discussion leading up to it: Can someone properly knowledgeable on the subject please explain whether the time dilation due to being in a gravitation ...
3
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1answer
107 views

Hermiticity of Dirac operator in curved spacetime

The Dirac Lagrangian in curved spacetime is usually given by \begin{equation} \mathcal{L} = i\bar{\Psi}\gamma^a e^{\mu}_a(\partial_\mu + \frac{1}{4}\omega_{\mu bc}\gamma^b\gamma^c)\Psi \end{equation} ...
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0answers
43 views

Problems of General Relativity on small and large scales [duplicate]

As far as I know, the most important problem of GR on large scales is the cosmological constant problem which in some manner can be thought of as a dark energy problem (please correct me if I am ...
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3answers
359 views

Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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5answers
5k views

How do I calculate the perturbations to the metric determinant?

I am trying to calculate sqrt(-g) in terms of a background metric and metric perturbations, to second order in the perturbations. I know how to expand tensors that depend on the metric, but I don't ...
3
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1answer
450 views

Casimir effect for spinning Casimir plates

I recently thought of the following experiment. Let's say I have two plates in vacuum facing each other. Now, due to the Casimir effect, there will be some internal attraction between the plates. Now ...
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1answer
63 views

Event horizon from the metric

Let us suppose we have a metric of this form $$ds^2=-A(r)dt^2+\frac{dr^2}{B(r)}+r^2d\Omega^2$$ In all documents I can read, I've seen that the event horizon is defined by considering $A(r)=0$ But I ...
7
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0answers
196 views

Does the spin of a particle change if observed from an accelerating reference frame?

If we consider a spin-$\frac12$ particle at rest in the absence of any potentials, we can use the Pauli spin operators and an associated basis to describe the observable. Let's arbitrarily choose the ...
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1answer
29 views

The equivalence principle and experiments concerning it?

Imagine that we are in a rocket accelerating with some magnitude $a_1 = dx^2/d^2t$, also imagine that we have a stationary rocket ship in close proximity to ours, stationary relative to our reference ...
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4answers
213 views

How do gravitational waves work without internal tension?

One implication of general relativity is the concept of gravitational waves or gravitational radiation, ripples in spacetime thought to travel at speeds close to the speed of light. As far as I have ...
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1answer
51 views

Does General Relativity say that the Laws of Physics are the same in all Reference Frames?

Most texts on General Relativity seem to imply that Einstein generalized the Relativity Principle (that all reference frames are equivalent) to include changes in velocity (accelerations); but then go ...
0
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1answer
85 views

Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold?

For $R_{\mu \nu \sigma \rho}$ the Riemann-tensor and $R$ the Ricci-scalar: Does $R_{\mu \nu \sigma \rho} R^{\mu \nu \sigma \rho} \propto R$ hold? Or is there any way to relate $R$ approximately ...
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0answers
15 views

Cosmological constant in General Relativity [duplicate]

According to my GR notes the cosmological constant can be thought of as a vacuum energy much in the same way as the ground state of the harmonic oscillator. The notes claim that the regularised energy ...
1
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1answer
54 views

Interpretation of black hole area

I'm studying properties of Kerr spacetimes and a lot of fuss is made about area of BH. It is defined to be integral of area element on event horizon $r=r_+$, $t=const.$ where $r_+$ is radial ...
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0answers
195 views

Black hole entropy from collapsed entangled pure light

Consider the following scenario, very similar to the one proposed in this question, but this time, the pure quantum radiation used for the black hole collapse, is now being split with down-converter ...
2
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2answers
70 views

Is it possible that one of the quasars we see is an ancient Milky Way?

As I understand it, even though our current measurements of the Riemann curvature of the universe overlaps with flat spacetime, this doesn't restrict the shape of the universe to being infinite. It's ...
18
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1answer
538 views

Positivity of Total Gravitational Energy in GR

I read the following statement in the introduction to an article: Over the last 30 years, one of the greatest achievements in classical general relativity has certainly been the proof of the ...
5
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1answer
548 views

How to calculate temperature and entropy on Schwarzschild-de Sitter space

The cosmological event horizon found in a de Sitter universe has some interesting similarities to that of a black hole. For example, since we can find a temperature at the horizon, we are able to use ...
7
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1answer
89 views

Does the background spacetime of a black hole affects its thermodynamic properties?

The question is this: will the thermodynamic properties of a black hole (Hawking radiation spectra and temperature, entropy, area, etc.) depend if the black hole sits in a DeSitter or an ...
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1answer
41 views

Why can only asymptotically flat and AdS black hole have the thermodynamics? What's about asymptoticaly dS black hole?

Almost all advanced GR textbooks will have the content of black hole thermodynamics for asymptotically flat black hole. And this paper solve the asymptotically AdS (Anti-de Sitter) black hole ...
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1answer
100 views

Does an object traveling near the speed of light create a gravitaional field? [duplicate]

Does a particle traveling near the speed of light create an observable/measureable gravitational field around it? I know most elementary particles travel near the speed of light and have no ...
1
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1answer
40 views

Short Gamma Ray Bursts from black hole mergers

I have read in passing that short gamma ray bursts can be caused by the merger of 2 black holes in a binary system. I have Googled but can't seem to find any good sources describing the phenomenon ...
5
votes
1answer
256 views

What kind of systems of black holes satisfy the laws of black hole thermodynamics?

I've come across black holes thermodynamics multiple times recently (both at this site and elsewhere) and some things started bugging me. For one thing, first law bothers me a little. It is a ...
18
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2answers
920 views

is there a way to split a black hole?

Classically, black holes can merge, becoming a single black hole with an horizon area greater than the sum of both merged components. Is it thermodynamically / statistically possible to split a black ...
3
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2answers
401 views

Hawking radiation and black hole entropy

Is black hole entropy, computed by means of quantum field theory on curved spacetime, the entropy of matter degrees of freedom i.e. non-gravitational dofs? What is one actually counting?
11
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1answer
1k views

Second Law of Black Hole Thermodynamics

I've been looking for a satisfying proof of this, and can't quite find it. I read the brief proof of the black hole area theorem in Wald, which is similar, but doesn't quite come down to the actual ...
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1answer
108 views

Difference of connections in the Killing vector equation

For the Killing vector equation, I sometimes see it written in terms of spin connection $\omega$ and other times in terms of the affine connection $\Gamma$. More clearly ...
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0answers
37 views

Equation of state of a universe full electrons

If I have a universe full of nothing but (slow moving) electrons, what would the equation of state ($w$, from $p=w\rho$) be? I think it would be incorrect to say that the electrons should be treated ...
0
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2answers
217 views

Does acceleration warp space?

I know that mass warps spacetime and gravity and acceleration are equivalent so does acceleration warp spacetime too?
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0answers
24 views

Gravitational boson violating relativity [duplicate]

Currently doing a introductory degree level physics course, they were talking about how changes in gravity/gravitational field cause changes so quickly that if you assigned it the "graviton" said ...
0
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1answer
73 views

Is it possible to directly test whether of not the vacuum gravitates?

According to GR, all sources of stress-energy (e.g. everything on the $T_{\mu\nu}$ side of the EFE) should gravitate (e.g. affect the curvature/$G_{\mu\nu}$ side of the EFE). We observe the expansion ...
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0answers
46 views

Any applications of kinetic physics on cosmological scales?

On galaxy cluster scales, one is usually forced to use approximate theories such as hydrodynamics or magnetohydrodynamics for modelling cosmological phenomena. I wanted to ask if kinetic theory is ...
2
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0answers
45 views

Thomas precession, Lie algebra of the Lorentz group and the conservation of energy

If you read this post Thomas Precession, you will see a very good answer by WetSavannaAnimal, on the subject of Thomas Precession, which I am currently working my through, in conjunction with some ...
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0answers
68 views

Existence of affine parametrization [closed]

This is a question from General Relativity by Wald Chapter 3, problem 5. Given either pseudo-Riemannian or Riemannian metric $g_{ab}$ and manifold $M$. Assume the $\nabla$ is compatible with the ...
6
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3answers
316 views

Is energy conserved in general relativity? Does $\nabla_aT^{ab}_{\rm matter}=0$ represent the conservation of energy and momentum?

For example, the radiation dominated cosmology, the energy density of radiation is proportional to $a^{-4}$ and the volume is proportional to $a^3$, where $a$ is the scale factor. So the total energy ...
3
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2answers
194 views

Speed of light and warp drives in general relativity

Velocities can be a tricky thing in general relativity. A cool concept seemly consistent with the Einstein field equations) is an Alcubierre drive, described by the Alcubierre metric. However, I ...
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1answer
99 views

How does a world line of an Alcubierre drive look like?

In my recent question ”Speed of light and warp drives in general relativity” I asked exactly how an Alcubierre drive worked and exactly what "FTL travel" meant. One of the comments I got stated that: ...
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0answers
79 views

Any textbook about non-renormalizability of gravity?

I have learned general relativity in a graduate-level. My knowledge about QFT is very rudimentary. But, I need to learn about non-renormalizability of gravity. I have these questions. Is there any ...
0
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1answer
58 views

Can everything be described without anything needing to actually “bend”? [closed]

Is space bending because gravity actually causes small particles to move differently? If large source of gravity is somewhere are particles extending towards it, creating a "bend" in space? So "bend" ...
4
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0answers
109 views

Angle sum of triangle in Schwarzschild solution

Curvature of space is often intuitively explained as angles of a triangle not adding up to 180 degrees. My questions concerns that. Suppose you have a perfectly spherical star of uniform density - so ...
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0answers
67 views

Variation of quadratic term in modified Einstein-Hilbert actions

In the context of mimetic gravity at some point one try to add to an already modified Einstein-Hilbert action also a term like $$ S_\chi=\int\,d^4x\,\sqrt{-g}\frac{1}{2}\gamma\chi^2,\qquad(\star) $$ ...
2
votes
6answers
368 views

Empty universe in the past, non-empty in the future

My question is the following. Are there solutions to the Einstein field equations, which have the property that there is a hypersurface of constant time and to the past of that surface space is empty ...
7
votes
3answers
219 views

Is every spacetime metric physically realizable?

Is every spacetime metric physically realizable? I know that given any spacetime metric, you could work out a stress-energy tensor for each position that would result in that metric. However, I also ...
1
vote
2answers
398 views

Does the actual curvature of spacetime hold energy?

My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
2
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1answer
61 views

Does spacetime curvature increase when an attractor's potential energy is converted to kinetic energy?

Imagine an asymptotically flat spacetime with nothing but two stars at a certain distance. They fall into each other and form one big star, so their potential energy is converted to kinetic energy. ...
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1answer
70 views

Mass and Schwarzschild Radius [duplicate]

Do free massless particles have a Schwarzschild radius? I'm curious about the mass in the equation for the Schwarzschild radius. I know that you can calculate a Schwarzschild radius for any massive ...
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1answer
43 views

Can you recover the values of spacetime intervals $s^2$ from given causal relations between events?

Given a suitable set $\mathcal S$ of events together with their (pairwise) causal relations, i.e. for each pair of distinct events $\mathsf A, \mathsf B \in \mathcal S$ the assignment whether ...