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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Will the rotation of a neutron star prevent it becoming a Black Hole?

This question, to me anyways, is basically a balancing act between 2 possibly opposing effects. Take a neutron star with just too small a mass to overcome it's degeneracy pressure, failing to ...
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35 views

Does the total particle energy increase in FRW Universe?

If a particle travels on a geodesic with 4-momentum $P^\mu$ in a spacetime with a Killing vector $K_\mu$ then we have a constant of motion, $K$, given by: $$K=K_\mu P^\mu$$ Using the relationships: ...
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73 views

Do Einstein's equations allow multiple solutions that agree in a neighborhood of a spacelike hypersurface?

This question is an extension of my a question that I have recently asked: Why doesn't a global frame of reference exist for GR?, where it was recommended that I post another question (so I am ...
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5answers
178 views

A ball in the gravity potential field of a black hole — seems a paradox

As illustrated in the following diagram (A, B, C, D are 4 specified space points, and C is close to a black hole), a small ball at distance of a black hole is stationary (suppose now it's mass is m0) ...
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3answers
152 views

Is an event horizon absolute to all observers?

Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon (disregarding effects of tidal ...
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1answer
66 views

Are moving objects producing stronger gravity fields? [duplicate]

If the strength of gravitational influence exerted by a body is derived from its mass and energy then is it true that a moving object which has some kinetic energy should also produce stronger ...
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0answers
21 views

Expansion of universe faster then speed of light? [duplicate]

Watching one of the shows on discovery channel, I got to know that during the starting phase of universe its speed should have been faster then speed of light. But then didnt einstein say that nothing ...
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1answer
118 views

What is the covariant basis around a Schwarzschild black hole?

First of all, I'm not interested in time for this question. So lets consider a 3-manifold whose metric is the spatial part of the Schwarzschild metric, so it has the event horizon and the singularity ...
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2answers
81 views

What experience tells us that gravitational acceleration cannot vanish everywhere?

In attempt to describe the consequences of the Equivalence Principle, Papapetrou in his book, said: When there are gravitational accelerations present, as for example in the gravitational field of ...
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2answers
59 views

Explosion in a sphere and the Gravitational field outside

Take a hollow sphere and conduct a process on the inside, which transfers mass into kinetic energy (e.g. we let a big nuclear bomb detonate or something like that). For simplicity, assume that this ...
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2answers
270 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 ...
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2answers
136 views

Why doesn't a global frame of reference exist for GR?

I only have at best a layperson's familiarity with GR, so forgive me if I am asking a basic question, but I have heard that in GR, we cannot have a global frame of reference, that is a frame of ...
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356 views

Alcubierre warp bubble effect on gravity and space

I read the question Faster-than-light communication using Alcubierre warp drive metric around a single qubit?, and these questions came to mind: What kind of impact would an Alcubierre warp bubble ...
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1answer
196 views

Higher-Dimensional Metrics in (Hyper)-Spherical Coordinates

I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical ...
2
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2answers
97 views

What is a Null Geodesic? [duplicate]

What is a Null Geodesic? My textbook only explains it as the Minkowski metric which equals to zero, but I'd appreciate a more detailed explanation.
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2answers
56 views

What kind of volume does the event horizon of a Kerr black hole enclose?

I'm sorry if this is a naive question, I'm not too good with General Relativity. I'm aware that a rotating black hole is described by the Kerr Metric, and black holes of this kind have ring ...
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6answers
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Thought experiment - would you notice if you fell into a black hole?

I've heard many scientists, when giving interviews and the like, state that if one were falling into a black hole massive enough that the tidal forces at the event horizon weren't too extreme, that ...
2
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1answer
66 views

Hawking Temperature of the BTZ Black Hole

The metric of the BTZ Black Hole is given by $$ ds^2 = - N^2 dt^2 + N^{-2} dr^2 +r^2(d\phi + N^\phi dt)^2 $$ with $$ N^2 = -M+ \frac{r^2}{l^2} + \frac{J^2}{4 r^2}, \ \ \ \ \ \ N^\phi = ...
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2answers
57 views

Stationary v/s Static

Blau, in his GR book, says that a stationary and spherically symmetric metric is automatically static. He says this easily follows from the fact that for a stationary metric, and in spherical ...
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0answers
8 views

Relativity Mass [duplicate]

How does mass increase as velocity approaches the speed of light? Why does the (relativistic) mass of an object increase when its speed approaches that of light?
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0answers
17 views

Why can't our universe be spherical? [duplicate]

if we happen to follow the bigbang singularity hypothesis, when he explosion occured shouldn't it expand in all directions. Seemingly our universe shouldn't have any boundaries. I searched for the ...
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0answers
54 views

Is the Big Bang notion compatible with the flat space? (A problem with the **moment** of Big Bang, not with the place of it) [duplicate]

A passage from a paper: "If one imagines running the clock backward in time, any given region of the universe shrinks and all galaxies in it get closer and closer until they smash together in ...
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4answers
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Why is the covariant derivative of the metric tensor zero?

I've consulted several books for the explanation of why $$\nabla _{\mu}g_{\alpha \beta} = 0,$$ and hence derive the relation between metric tensor and affine connection $\Gamma ^{\sigma}_{\mu ...
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1answer
135 views

$U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
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2answers
63 views

Different signatures

I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I ...
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1answer
155 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 ...
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How could general relativity and quantum mechanics ever be combined? [duplicate]

Maybe I'm mistaken but here it's what I understand: Einstein's theories have to do with space time curvature. Whilst quantum mechanics has to do with probabilities. The solutions to the Shrodinger ...
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423 views

What different approximations yield Gravitoelectromagnetism and Weak Field Einstein Equations?

This question is inspired by this answer, which cites Gravitoelectromagnetism (GEM) as a valid approximation to the Einstein Field Equations (EFE). The wonted presentation of gravitational waves is ...
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1answer
37 views

Calculating time dilation

I'm writing a science fiction story where the protagonist's experience requires long intervals between events. My plan is to put him/her/it on a spaceship between events at an appreciable percentage ...
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2answers
71 views

How to show flat FRW metric has a time-like conformal Killing vector?

I would like to derive the fact that the flat FRW metric has a time-like conformal Killing vector. Is there an easy way to do this? @ValterMoretti showed how one can do this for metrics with a ...
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1answer
46 views

Is a planets orbit really a straight line through curved spacetime? [duplicate]

My understanding is that general relativity concludes that gravity isn't real because it does not exist in all frames of reference. Also that mass and energy warp spacetime into a curved geometry. ...
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3answers
72 views

Relativistic rigid motion

In Bryce DeWitt's Lectures on Gravitation, in eq. 2.7 on page 25 when he describes the rigid motion of a continuum he states $$x^\mu(\xi,\tau)=x^\mu(0,\sigma)+\xi^in^\mu_i(\sigma)\,\,\,(i=1,2,3) \, ...
3
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1answer
348 views

Gravity's Rainbow

What is it? I've seen it in context of a few research papers such as Absence of black holes at LHC due to gravity's rainbow and Thermodynamics of black holes in gravity’s rainbow formalisms My best ...
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1answer
275 views

What kind of object is the Landau--Lifshitz pseudotensor?

I understand that it's called a pseudotensor because it's not a tensor. Wikipedia says most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR. ...
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3answers
107 views

Does it make sense to model the Universe from an outside perspective? [closed]

I was reading some questions and answers about black holes and whether matter can actually pass through the apparent horizon, in particular this one: How can anything ever fall into a black hole as ...
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1answer
64 views

Time dilation and space time [closed]

I know a little about space time, and I know that space time is adding the time component into the three- dimensional world and creating an abstract universe. But my question is that why time is ...
0
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1answer
62 views

Can gravitational waves carry momentum, and if so what mass/energy produces it, and is space-time capable of vortex formation?

This question is about gravitational waves postulated by Einstein. Is gravitational radiation a form of mass/energy that can form momentum? If it causes ripples in space-time, would space-time ...
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3answers
56 views

Energies of bodies travelling on different geodesics

If two bodies of equal mass are released at rest from point $A$ and travel on different geodesics in a curved spacetime to point $B$ will they have the same total energy at point $B$? Is the same ...
7
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1answer
139 views

Kerr solution for finite collapse time

The Kerr black hole solutions gives an analytic continuation that is asymptotically flat. Some people have argued that this is another universe, but others state that the analytic continuation ...
3
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2answers
87 views

Can I simply reverse the indices in a contraction?

Suppose I have something like $$ \left( \nabla_\mu \nabla_\beta - \nabla_\beta \nabla_\mu \right) V^\mu = R_{\nu \beta} V^\nu $$ Can since all the terms involving $\mu$ on the left and $\nu$ on the ...
3
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0answers
78 views

Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. ...
2
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2answers
97 views

How are FRW metric and Minkowski metric physically different?

According to GR, matrices are coordinate invariant. Does this mean we can transform FRW metric to Minkowski metric with a coordinate transformation like $$dx'=dx\cdot a(t), dy' = dy\cdot a(t), dz' = ...
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0answers
92 views

Basic doubt on the philosophy of Quantum field theory and General relativity

As I understand, the basic idea of General relativity is that the 4-d spacetime is "deformed" because of the presence of matter-energy, in other words no pre-existing (or background) space is assumed ...
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0answers
45 views

Conformal time-like Killing vector near null geodesics in all spacetimes?

Is it true that in all spacetimes there is some conformal time-like Killing vector $\tau^a$ in the vicinity of null geodesics? If the above statement is true then can one argue that, for all ...
6
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1answer
716 views

Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial ...
2
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0answers
117 views

Precession of Mercury (Python simulation)

I was trying to simulate the precession of Mercury based on the perturbed solution, and my questions about its implementation in python can be seen here: ...
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2answers
124 views

What is the experimental evidence that suggests space-time is curved?

Sorry, if this is a stupid question. tl;dr: Skip to the last paragraph for the question. I know curved space-time is one way to express gravity and so far it seems to work well. I still need a lot ...
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61 views

Does GR put a theoretical lower limit on the radius of a black hole event horizon?

Within GR theory, without going to the extreme r/0 as a radius, (but approaching that as an asymptotic case), is there any theoretical limit as to how small the event horizon of a rotating and/or ...
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2answers
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Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com: