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.

learn more… | top users | synonyms (1)

13
votes
1answer
593 views

How does one measure space-like geodesics? Or: What is the physical interpretation of space-like geodesics?

In general relativity, time-like geodesics are the trajectories of free-falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure ...
6
votes
2answers
451 views

How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...
0
votes
0answers
77 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
5
votes
2answers
316 views

Exterior (covariant) derivatives and electromagnetism

I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the ...
1
vote
1answer
146 views

How to make a black hole?

Many Physics discussions I have often conclude with: Well you will then form a black hole... My questions are: Is there a general recipe for making a black hole? If not, then can you list the ...
0
votes
1answer
139 views

How to show that value is conserved along geodesics?

Let's have the motion of charged particle in a field of Reissner-type black hole. The equation of motion looks like $$ \frac{d^{2}x^{\mu}}{d \tau^{2}} + \Gamma^{\mu}_{\nu \lambda}\frac{dx^{\nu}}{d ...
5
votes
4answers
287 views

Is there a distinguished reference system, after all?

The equivalence principle, being the main postulate upon which the general relativity theory rests, basically states that all reference systems are equivalent, because pseudo forces can (locally) be ...
2
votes
1answer
79 views

Why must the final state be stationary?

I faced the following sentences: We consider a gravitational collapse taking place in this spacetime. The singularity theorems assure us that a singularity will form. The assumption that the ...
2
votes
2answers
279 views

How does the Einstein Equivalence Principle imply a spacetime with a metric (and a connection)?

I have at hand the book by Clifford Will, "Theory and Experiments in Gravitational Physics", and the following Living Reviews in Relativity article. He quotes the Einstein Equivalence Principle (EEP) ...
1
vote
0answers
33 views

If the absolute horizon were exclusionary of matter, what supernova behaviors would that predict?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.415, Box 12.1: ... The absolute horizon is just a point when created, but it then expands smoothly, like a balloon being blown up, ...
14
votes
3answers
376 views

Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
2
votes
0answers
30 views

What is the total mass of the accelerated viewpoint particle atmosphere of a black hole?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.443, just above Figure 12.5: Surprisingly, from the accelerated viewpoint, the vacuum fluctuations consist not of virtual particles ...
2
votes
1answer
161 views

If charged particles always attach to black hole event horizons, how can ordinary matter fall in?

(A friend at work kindly loaned me loaned me his copy of Kip S Thorne's "Black Holes & Time Warps". This may have been ill-advised... :) BH&TW 1994 paperback p.410 Figure 11.5: ... all ...
2
votes
2answers
187 views

On the singularity $r=0$ of the Schwarzschild metric

I faced following sentences: Unlike the co-ordinate singularity at $r = 2M$, the origin of the Schwarzschild metric $r = 0$ has a true curvature singularity. It was first believed that this ...
3
votes
1answer
474 views

What's the importance of conformal transformations in general relativity?

I tried to understand the importance of conformal transformations in general relativity, but I failed. I didn't see that conformal transformations help to simplify the metrics, and also I didn't see ...
4
votes
1answer
165 views

Effective mass of a black hole?

Suppose a black hole forms from a given mass of particles such as the core of a star going supernova. The black hole formed will have an effective mass due to the curvature of space time induced. Such ...
-2
votes
1answer
190 views

Helical Particle Waves? [closed]

[Helical Particle Waves][1] Helical Particle Waves: http://www.heliwave.com/gaasenbeek/spap1.html In the link above someone explains a new theory that explains the general relativity and quantum ...
4
votes
1answer
261 views

What is the effect of gravity on gamma rays?

I read an article about a Gamma Ray burst linked to a black hole. How does high gravity fields affect gamma rays?
1
vote
1answer
371 views

Time dilation in a gravitational field and the equivalence principle

A clock near the surface of the earth will run slower than one on the top of the mountain. If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in ...
8
votes
2answers
300 views

What is the condition for accelerating charge to radiate?

I was always taught that any accelerating charge produces radiation, but I don't think this condition is sufficient condition. For instance, any free charge on Earth is accelerated due to Earth ...
4
votes
3answers
452 views

In the static spacetime, the extrinsic curvature of hypersurface $t=constant$ is zero

How can I prove that in the static spacetime, the extrinsic curvature of hypersurface $t=constant$ is zero? My efforts all are failed. Any hint would be greatly appreciated.
12
votes
3answers
593 views

Is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations?

I know that scaling the action with a non-zero multiplicative constant, or adding a total divergence term to the Lagrangian density do not change the Euler-Lagrange equations, cf. e.g. this ...
-3
votes
2answers
120 views

What does Mass bend? [closed]

Mass and Energy can warp space-time around them, but that doesn't answer what space-time is, what is space?
1
vote
4answers
251 views

Equivalence principle and acceleration vs a gravitational field

I picked this up on the net: Einstein came to realize the principle of equivalence, and it states that an accelerated system is completely physically equivalent to a system inside a gravitational ...
2
votes
1answer
338 views

A Competitor for General Relativity? [closed]

GR stands alone in its ability to pass both weak and strong field tests of gravity fields. From 1905 to 1915, there was renewed interest in a somehow modified scalar field theory. Here is the ...
0
votes
0answers
109 views

How to use The Schwarzchild Metric formula to get distribution representing “free-fall”

Given formula: How I can use to calculate distribution of points in space, so if i choose path which contains most of the points I get path that close to "free-fall path". As far as I know i should ...
2
votes
1answer
442 views

The Weyl tensor and gravitational waves

How exactly is the Weyl tensor is connected with information about gravitational waves? And what are physical reasons for that?
2
votes
0answers
70 views

To what extent are the astronomically observed black hole candidates compatible with GR black holes?

Do they all fit Schwarzschild black holes? How people compare them with more complicate BH solutions as spinning BH solutions (even if they are not known analytically), say. I'd like more than ...
5
votes
3answers
435 views

Did people realize that gravity accelerated things before Einstein's elevator thought experiment?

I'm reading about the (very near) equivalence of gravitational mass and inertial mass in my undergrad GR course, and the text (Lambourne) describes this equivalence as the inspiration for Einstein's ...
2
votes
1answer
175 views

Is any apparent horizon a minimal surface?

I faced "any apparent horizon is a minimal surface", but I don't know how I can relate a physical concept (apparent horizon) to pure mathematical concept (minimal surface). How can I prove it?
2
votes
1answer
198 views

Proper time in Nordstrom gravity

This wikipedia article claims that there are two interpretations of Nordstrom's scalar theory of gravity: 1) A scalar field theory on flat space. The reason why an apple falls is that its mass is ...
4
votes
1answer
150 views

Some hints for special case of metric tensor in GR

Let's have metric $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2 - 2f(t - z, x, y)(dt - dz)^2. $$ I need to prove that it is an exact solution for Einstein equations in vacuum for $\partial_{x}^{2}f + ...
3
votes
1answer
87 views

Question about simple permutation of covariant derivatives

I must to compute value $$ [[D_{\mu}, D_{\nu}],D_{\lambda}]A^{\rho}. $$ It is equal to $$ [D_{\mu}, D_{\nu}]D_{\lambda}A^{\rho} - D_{\lambda} ([D_{\mu}, D_{\nu}]])A^{\rho} - [D_{\mu}, ...
2
votes
2answers
262 views

Why do we must know the Weyl tensor for 4-dimensional space-time?

I heard that we must know the Weyl tensor for fully describing the curvature of the 4-dimensional space-time (in space-time with less dimensions it vanishes, so I don't interesting in cases of less ...
4
votes
0answers
586 views

How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
1
vote
1answer
113 views

Mass is rigidity?

In General Relativity, a totally rigid body cannot be accelerated. It will behave like something of infinite mass. Similarly a body of two separated particles which connected to each other with a ...
0
votes
0answers
36 views

Good and simple reference for studying about ADM mass [duplicate]

I need a good and simple reference for studying about ADM mass. Can someone introduce me one?
6
votes
6answers
1k views

Physical meaning of non-trivial solutions of vacuum Einstein's field equations

According to Einstein, the space-time is curved and the origin of the curvature is the presence of matter i.e. the presence of the energy-momentum tensor $T_{ab}$ in Einstein's field equations. If our ...
0
votes
0answers
115 views

On motivation for the definition of ADM mass

The ADM mass is expressed in terms of the initial data as a surface integral over a surface $S$ at spatial infinity: $$M:=-\frac{1}{8\pi}\lim_{r\to \infty}\int_S(k-k_0)\sqrt{\sigma}dS$$ where ...
2
votes
1answer
576 views

In an absence of gravity, does time flow faster or slower than on Earth? [duplicate]

I understand from my very limited knowledge of relativity that an object traveling at relativistic speeds essentially experiences the progression of time slow to a crawl. Since, according to ...
3
votes
1answer
755 views

Are there any good video lectures for learning general relativity at the level of Hobson?

Before answering, please see our policy on resource recommendation questions. Please try to give substantial answers that detail the style, content, and prerequisites of the book or paper (or ...
4
votes
0answers
176 views

What is the radius of convergence of the Fefferman-Graham expansion?

There is this general result that for any metric $ds^2$ that is asymptotically $AdS_{d+1}$, then there is a coordinate system in which $$ ds^2 = \frac{1}{r^2}(dr^2 + g_{ij}(r,x^k)dx^i dx^j) $$ where ...
3
votes
0answers
366 views

Gauss-Bonnet term in Physics

Given a 4-dimensional compact manifold (torsion free), the Euler characteristic is defined as: $$E_4 ~=~ \int \epsilon_{abcd}R^{ab} \wedge R^{cd}$$ with $R^{ab}$ is the curvature 2-form. Perturb the ...
2
votes
2answers
777 views

About the standard derivation of the gravitational redshift

The objective is to derive the gravitational redshift ONLY from the Einstein's equivalence principle (E.E.P.), without using the whole theory of Relativity. This is the standard "informal" derivation ...
1
vote
0answers
143 views

Linearized gravity and symmetries

I have naive question. When we analyzing weak gravity field we introduce expression for metric tensor as $$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}, \quad \eta_{\mu \nu} = diag(1, -1, -1, -1), ...
5
votes
3answers
221 views

Is isotropy a fundamental/invariant feature of our universe, or is it merely a convenient, albeit arbitrary, feature of some reference frames?

This is related to a previous post. Assuming that the Cosmological Principle is correct, does this imply that the universe possess an empircially privileged reference frame? What I am trying to ...
2
votes
1answer
359 views

Ricci scalar in Scalar Field in Curved Space-time

I was recently looking at a Lagrangian of a scalar field in curved space-time at http://www.unc.edu/~mgood/research/Carroll_QFT_CS.pdf on page 8. I am not a physicist, and I am currently studying ...
9
votes
2answers
584 views

Assuming that the Cosmological Principle is correct, does this imply that the universe possess an empirically privileged reference frame?

OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so ...
1
vote
0answers
78 views

River model of spacetime for arbitrary situations

This paper describes black holes as space flowing inward (the rotating hole also twists in a weird way): http://arxiv.org/abs/gr-qc/0411060 The proper time given by the objects is the same as ...
-1
votes
1answer
239 views

Recommended book for beginners on advanced science topics [duplicate]

I have a background in engineering so I have some familiarity with basic math and science. I've recently been reading about other topics such as Einstein's relativity and have become interested in ...