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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where the proper time is invariant why $d\tau$ is not zero?

where the proper time is invariant why change (differential) in proper time $d\tau$ is not zero? $\Delta \tau=\tau_f-\tau_i$ as i know. $d(invariant)=0$ note to comment: action $S=-m_oc^2\int_C d\tau$ ...
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1answer
135 views

Can the zeroth-component of a 4-velocity be negative?

Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks. This is referring to $V^0$ for a curved space ...
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1answer
382 views

Homogeneous gravitational field and the geodesic deviation

In General Relativity (GR), we have the geodesic deviation equation (GDE) ...
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2answers
2k views

How can mass affect spacetime?

In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?
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1answer
181 views

Massless Dirac equation is Weyl covariant

Does somebody know how to show that the following equation is Weyl invariant? $$\gamma^ae_a^\mu D_\mu \Psi=0$$ where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
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1answer
715 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 ...
6
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1answer
423 views

Diffeomorphisms and boundary conditions

I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper. I found this ...
2
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2answers
253 views

Curved space or curved spacetime?

As I understand it, you can have time + flat space = curved spacetime. So, when one is trying to emphasise that there is a curvature to the space, is it more technically correct to say curved space ...
3
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1answer
675 views

Dirac Equation in General Relativity

Dirac equation for the massless fermions in curved spase time is $γ^ae^μ_aD_μΨ=0$, where $e^μ_a$ are the tetrads. I have to show that Dirac spinors obey the following equation: ...
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0answers
118 views

Showing that the Ricci scalar equals a product of commutators

I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
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1answer
186 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 ...
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2answers
657 views

What is 'past null infinity'?

For example, in the sentence "there is no incoming radiation at past null infinity".
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1answer
504 views

How does one write the Einstein field equations in terms of Ricci tensor?

How can I go from the 'standard' Einstein equations $R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu}$ to these equations: $R_{\mu\nu} = \frac{8\pi G}{c^4}(T_{\mu\nu} - ...
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2answers
384 views

Stellar winds from neutron stars

It seems that this question has not really been explored in the literature. Do isolated neutron stars (which do not accrete material) emit stellar wind? If yes, what composition would it have? If yes, ...
4
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2answers
385 views

How does the evaporation of a black hole look for a distant observer?

Let's assume an observer looking at a distant black hole that is created by collapsing star. In observer frame of reference time near black hole horizon asymptotically slows down and he never see ...
6
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2answers
468 views

What is the “foamy space” hypothesis that has been debunked recently?

In "Space-Time Is Smooth, Not Foamy", a Space.com article, it is stated: In his general theory of relativity, Einstein described space-time as fundamentally smooth, warping only under the strain ...
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2answers
602 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
6
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1answer
366 views

Does conformal gravity explain the Bullet cluster lensing effects?

Conformal gravity is an "alternative" theory of gravity, where instead of using the Einstein-Hilbert action composed of the Ricci scalar, the square of the conformal Weyl tensor is used. It was ...
4
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3answers
407 views

Question on inflation

I have two particular questions regarding the inflationary scenario. They are: 1.) What is the physical origin of the inflaton field? 2.) Why has the potential of the inflation field its particular ...
13
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5answers
2k views

Does the amount of gravitational potential energy in the universe increase as it expands?

It seems to me that extra gravitational potential energy is created as the universe expands and the distance between massive objects such as galaxy clusters increases; this implies that energy is not ...
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0answers
169 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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1answer
245 views

Killing Vectors of BTZ black hole and their calculation in general

I was wondering what are the Killing vectors of BTZ black hole and how to guess them easily? Will it be the same as of AdS? What then will be Killing vectors for AdS-Schwarzschild e.g.?
3
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1answer
312 views

Question on inflation as a phase transition

I have just finished watching the following video http://www.youtube.com/watch?v=beQ9fZ0jVdE where Laughlin, Gross and some students discuss e.g. about inflation. The following question is risen: Is ...
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2answers
213 views

Can time dilation be explained by limitations on computing power?

Are there any ideas of explaining the time dilatation as limits in "computing power"? What I mean is basically that the greater is a concentrated mass, the harder is to "compute" what happens in such ...
2
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1answer
312 views

Would dense matter around a black hole event horizon eventually form a secondary black hole? [duplicate]

Possible Duplicate: Black hole formation as seen by a distant observer Given that matter can never cross the event horizon of a black hole (from an external observer point of view), if a ...
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0answers
53 views

Can a black hole actually grow, from the point of view of a distant observer? [duplicate]

Possible Duplicate: Black hole formation as seen by a distant observer I've read in several places that from the PoV of a distant observer it will take an infinite amount of time for new ...
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1answer
368 views

How to find the intrinsic covariant derivative component?

How to find the intrinsic covariant derivative component? In general relativity the elements of the acceleration four-vector are related to the elements of the four-velocity through a covariant ...
3
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1answer
506 views

How would you detect Hawking radiation?

Hawking theorized that a black hole must radiate and therefore lose mass (Hawking radiation). According to classical relativity though, nothing can escape a black hole, the hawking radiation would ...
1
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1answer
2k views

In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?

I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a ...
6
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1answer
192 views

Einstein's equations as a Dirichlet boundary problem

Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem? I am thinking of something along those lines: Consider a compact manifold $M$ ...
2
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1answer
452 views

Curiosity episode with Stephen Hawking. The Big-Bang

In an episode of Discovery's Curiosity with host Stephen Hawking, he claims the Big Bang event can be explained from physics alone, and does not require the intervention of a creator. 1) His ...
11
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4answers
5k views

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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5answers
1k views

The definition of an inertial reference frame in Einstein's relativity

I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the ...
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4answers
2k views

What is the exact gravitational force between two masses including relativistic effects?

I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 ...
4
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2answers
229 views

Is Brian Cox right to claim that Gravity is a strong force for large masses, is it wrong, or is it only a matter of interpretation?

I watched a program of his in which it was claimed that since mass bends space in accordance to General Relativity, then in the case of very large stars it becomes a strong force to the point of being ...
4
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2answers
456 views

Black hole formation as seen by a distant observer [duplicate]

Possible Duplicate: How can anything ever fall into a black hole as seen from an outside observer? Is black hole formation observable for a distant observer in finite amount of time? ...
13
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3answers
602 views

Extremal black hole with no angular momentum and no electric charge

A black hole will have a temperature that is a function of the mass, the angular momentum and the electric charge. For a fixed mass, Angular momentum and electric charge are bounded by the extremality ...
4
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1answer
96 views

Could a bipolar nebula be produced by a time gradient?

M2-9 is an example of a bipolar nebula that resembles two back-to-back rocket nozzles. Is it possible that this shape (somewhat unusual for an explosion) is the result of a time gradient? A rotating ...
2
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2answers
232 views

Gravitation force- Attraction and repulsion

Gravitation force is always attractive. Now assume(not a practical one): I took our Earth in my hand and started shaking up and down. This will create a disturbance in space-time warp and it moves ...
4
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0answers
277 views

Conservation of Energy in the Universe [duplicate]

Possible Duplicate: Is energy really conserved? Why can’t energy be created or destroyed? One of the laws of the universe that dazzles me the most is the law of conservation of energy. I ...
8
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1answer
892 views

Diffeomorphisms, Isometries And General Relativity

Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while. Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
12
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2answers
1k views

What is the weight equation through general relativity?

The gravitational force on your body, called your weight, pushes you down onto the floor. $$W=mg$$ So, what is the weight equation through general relativity?
1
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0answers
101 views

Does quantum Zeno effect play role in astrophysics?

For example, do two galaxies situated in proximity reduce the atom decay rate in each other? What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
4
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0answers
118 views

Alternate geodesic completions of a Schwarzschild black hole

The Kruskal-Szekeres solution extends the exterior Schwarzschild solution maximally, so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction. ...
2
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3answers
647 views

Are the principles of space-time homogeneity and Isotropy independent of one another?

Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
6
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1answer
77 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 Anti-DeSitter ...
21
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2answers
607 views

Does a charged or rotating black hole change the genus of spacetime?

For a Reissner–Nordström or Kerr black hole there is an analytic continuation through the event horizon and back out. Assuming this is physically meaningful (various site members hereabouts think ...
4
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3answers
415 views

Could metric expansion create holes, or cavities in the fabric of spacetime?

Is it possible for metric expansion to create holes, or cavities in the fabric of spacetime? According to the Schwarzschild metric, the metric expansion of space around a black hole goes to infinity ...
5
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2answers
413 views

Space-time geometry and metric

I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
5
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2answers
312 views

Is this closed time-like curve in a Godel universe a “circle”?

Would the observer moving along the circle in this Godel space-time diagram feel fictitious forces as though he is accelerating along a circular path or would he simply arrive at an earlier point in ...