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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12
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2answers
506 views

Doesn't the Schwarzschild metric combined with Hawking radiation imply that nothing ever gets past the event horizon of a black hole?

According to the General Theory of Relativity, the coordinate time distance per spacetime distance traveled by a particle freely falling into a black hole gets closer and closer to $0$ as the particle ...
1
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0answers
29 views

Geodesic tangent vector in a Riemannian 4-space

I am doing a question in Lewis Ryder's introduction to General relativity. I am very close to the answer but not quite there. The question is: A Riemannian 4-space has metric $$ds^2 = ...
4
votes
4answers
198 views

Binary black hole merger viewed from inside the event horizon

How did the metric evolve inside the event horizons of the black holes whose merger caused the GW150914 signal? In principle the Schwarzchild metric of a non-rotating black hole is known inside the ...
-1
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0answers
28 views

What are the effects of relativity on the universe itself? [on hold]

I'm obviously not anything like an expert on the subject, but it occurs to me that the relativity of objects or lack thereof would affect the environment around it. Time moves fastest when there is ...
1
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1answer
60 views

On the proof of the existence of geodesics coordinates

From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is $$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} ...
0
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2answers
123 views

Is this analogy of Hawking Radiation correct?

Through reading of textbooks and other research papers, I have settled on the analogy of hawking radiation below (Written completely by myself) Within the ergosphere of the black hole, virtual ...
4
votes
3answers
868 views

What is / are the primary criticism(s) against Einstein-Cartan-Evans field theory?

What is / are the primary criticism(s) against Einstein-Cartan-Evans (ECE) field theory? On Wikipedia the references provided were: arXiv:physics/0607186, MR2372785 (2008j:83049b), MR2218579 ...
2
votes
1answer
415 views

Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= ...
-1
votes
0answers
47 views

If Black Holes Consume Space What Is The Space Traversing? [duplicate]

I've heard it stated by physicists that space moves into (Or through/down into if you like) black holes faster than the speed of light and that this is possible because the speed of light is a ...
50
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15answers
28k views

Getting started self-studying general relativity

What are some good books, videos, websites for getting started with general relativity? I would prefer mathematically rigorous sources.
0
votes
0answers
21 views

Newtonian limit of the Einstein Equation for the Schwarzschild metric [closed]

I am trying to get the Newtonian limit of the Einstein Equation for the Schwarzschild metric $$ ds^2 = \left(1 - 2\phi(r) \right) dt^2 - \left(1+2\phi(r)\right) dr^2 - r^2 \left(d\theta^2 + ...
1
vote
1answer
33 views

Eddington-Finkelstein coordinate

The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as \begin{align} u&=t-r^*\\ v&=t+r^* \end{align} where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$ The ...
3
votes
1answer
46 views

Is this equation $\nabla_a\sqrt{-g}=0$ correct? [duplicate]

Is the equation $$\nabla_a\sqrt{-g}=0$$ correct? Here $\nabla_a$ is the Levi-Civita connection, and $g$ is the determinant of metric $g_{ab}$. Apparently, we have $\nabla_ag_{bc}=0$, but I am not sure ...
7
votes
2answers
213 views

Bending of light - photon's inertia instead of mass

Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to ...
0
votes
0answers
22 views

Dark matter from general relativity? [duplicate]

We know that there is dark matter due to the observational orbital velocities and mass to light ratio not matching that of expected ones. However the expected orbital velocities of stars in the Milky ...
1
vote
0answers
21 views

what is the metric of N-sheeted $AdS_3$?

Suppose the AdS$_3$ metric is given by $$ ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2 $$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications ...
53
votes
4answers
3k views

GR and my journey to the centre of the Earth

[General Relativity] basically says that the reason you are sticking to the floor right now is that the shortest distance between today and tomorrow is through the center of the Earth. ...
-1
votes
1answer
48 views

What are the vacuum Einstein's equations? [closed]

I read on Wikipedia that if the Stress-Energy Tensor is set to zero in General Relativity's Field Equation that it makes the Vacuum Equations. What are these equations, and how are they used?
1
vote
0answers
31 views

What is the Metric Tensor? [duplicate]

I was studying Einstein's Field Equation, and this was the most common symbol. Can you explain what it is and how it could be used?
0
votes
0answers
14 views

When a dumbbell tumbles, is the gravitational wave amplitude dependent on the frequency?

Normally, we think of gravitational waves as being only created by massive objects, which makes using them infeasible. But if the speed of tumbling affects the amplitude of the waves, then we might ...
1
vote
1answer
46 views

Orthogonal of tangent vector in Rindler coordinates

For 2D space time from $(t,x)$ to $(u,v)$ the transformation are $$t = u \sinh(v)$$$$x=u\cosh(v)$$ Asking to show that two families of curves $u = \textrm{constant}$ and $v = \textrm{constant}$ ...
0
votes
1answer
75 views

Which comes first for gravity: mass or space-time? [closed]

According to current theory, matter warps space-time and creates gravity. The Einstein field equations EFE describe the fundamental interaction of gravitation as a result of spacetime being curved by ...
32
votes
1answer
2k views

Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
2
votes
2answers
429 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
4
votes
3answers
70 views

Where does the energy of a photon trying to escape a black hole go?

I've heard "light cannot escape a black hole" explained several ways. One is that if a photon inside the event horizon tries to escape a black hole it loses energy to gravity. As it loses energy its ...
3
votes
3answers
178 views

Why does matter curve space time? [duplicate]

I am under the impression that Einstein never explains in his General Theory of Relativity, why matter curves spacetime; could explanations please be given?
1
vote
0answers
28 views

Null geodesics in uniform gravitational field metric

I'm trying to understand the null geodesics in the metric: $$\mathrm{ds}^2 = -(1+gz)^2 \mathrm{dt}^2 + \mathrm{dz}^2 + \mathrm{dx}^2$$ In particular I'm wondering if the following intuition is ...
4
votes
2answers
114 views

Why is the covariant derivative of the determinant of the metric zero?

This question, metric determinant and its partial and covariant derivative, seems to indicate $$\nabla_a \sqrt{g}=0.$$ Why is this the case? I've always learned that $$\nabla_a f= \partial_a f,$$ ...
0
votes
0answers
19 views

How are negative energy orbits around a Black Hole defined?

I have read several times that within the ergosphere or a Kerr Black Hole, it is possible to have particles that have an orbital energy value of less than 0. However, I do not understand the concept ...
0
votes
1answer
77 views

At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
2
votes
1answer
251 views

How would it be to look at the sky if the earth were near the edge of the universe?

By looking at this picture: http://earthspacecircle.blogspot.com/2013/01/earths-location-in-universe.html The earth is near the center of the universe. I've read that the universe look the same no ...
7
votes
1answer
200 views

Homotopy proof of the lack of foliation of the Gödel metric

A common proof of the lack of foliation of the Gödel universe, apparently mostly copy pasted from Hawking and Ellis, goes thusly : A closed timelike curve must cross a spacelike hypersurface ...
5
votes
1answer
275 views

Can tachyons escape the gravitational pull of a classical black hole?

Anything that crosses the event horizon of a black hole cannot escape the pull since it has crossed the Schwarzschild radius and thus, the escape velocity is greater than the speed of light, and since ...
3
votes
1answer
37 views

$f^{\prime}(R)=0$ in $f(R)$ gravity

Suppose in a certain $f(R)$ gravity theory, $f^{\prime}(R)=0$ for some finite value of $R$. (e.g. let $f(R)=R+\alpha R^2$ with $\alpha<0$. $f^{\prime}(R)=0$ at $R=-\frac{1}{2\alpha}$.) Also ...
3
votes
2answers
586 views

Producing gravitational waves in labs

Can gravitational waves be created on very small region of vacuum with quadruple movement of atom or subatomic particles?
3
votes
2answers
247 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
4
votes
1answer
224 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
-8
votes
1answer
82 views

Smallest thing ever measured and quantum mechanic bs [closed]

Is it possible to prove in 2016 that the universe is made up of more discrete units than say an atom or quark? What is the smallest thing we have been able to measure, like not theorize about, but ...
-3
votes
0answers
38 views

General theory of relativity proves beginning of the universe? [duplicate]

As I'm not a physics student, i only have some basic idea about how the theory works. As Hawking quoted in his book - "A brief history of time " Roger Penrose and I showed that Einstein’s ...
7
votes
1answer
328 views

Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
3
votes
1answer
126 views

Distance between two galaxies of different redshift

Let $Q_1$ and $Q_2$ two different objects in the Universe (we can think to two galaxies or quasars), that we observe from the Earth at different angular position $(\alpha_1,\delta_1)$, ...
0
votes
3answers
59 views

Space time curvature and gravity [duplicate]

Is Space time curvature responsible for gravity or Gravity responsible for the curvature in space-time.
0
votes
0answers
38 views

Proper Distance and Coordinate Distance in General Relativity

When I started studying general relativity,I was told that the coordinate distance is not covariant and it does not have any physical meaning.I realized that only the proper length is the ...
3
votes
0answers
19 views

Israel-Wilson-Perjés Solutions

I'm searching for a reference that gives explicitly the field strength (or at least the gauge fields) of the Israel-Wilson-Perjés Solution, using complex harmonic functions for the metric. In ...
2
votes
1answer
74 views

What is the utility of ADM decomposition of the space-time metric?

I know it's one of the possibility of quantization of gravitational field's degree of freedom but it is introduced also in other situation. My question is what is the use for this kind of ...
5
votes
2answers
266 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
6
votes
2answers
383 views

Wave packet in curved spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
4
votes
2answers
100 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
2
votes
1answer
121 views

Two spherically symmetric shells of matter collapsing into a black hole

Suppose I have a thin spherically symmetric shell of matter of (rest) mass $M$ that collapses to form a black hole, and later a second thin spherical shell of mass (rest) $M'$, concentric to the ...
1
vote
0answers
25 views

Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields \begin{equation} S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} , \end{equation} ...