A theory that describes how matter produces and responds to 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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Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...
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2answers
145 views

Speed of light in a gravitational field ?

How do I solve the speed of light in gravitational field? Should I just add gravitational acceleration in speed of light? $c'=c_0+g(r)t$?
2
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1answer
150 views

Does the total mass of an isolated object include the mass stored in its gravitational field?

Since neither the object nor its field could exist without the other, it would seem strange not to include the field energy as part of the object. But how exactly does the accounting go? How is the ...
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1answer
65 views

Relativity question: frequency shift under constant acceleration

Okay, my buddy tells me this: Let there be a starship, ovoid, and me and my buddy stand each at the extremities of the ship, him below the roof, me on the floor. We start a journey and the ship ...
2
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1answer
59 views

Finding superpotentials and central charges in $AdS_3$

In text "Covariant theory of asymptotic symmetries, conservation laws and central charges" is given an example of finding central charges and superpotential (among other things). I am interested in ...
7
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1answer
113 views

Does Hawking radiation break asymptotic flatness?

Basically what the question says -- there is reason to expect that, if allowed to continue long enough for the radiation to reach future null infinity, the fact that the radiation will fall off at ...
4
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0answers
79 views

Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: The effects of Wheeler's quantum foam on black hole growth are explored from an ...
0
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1answer
74 views

How does the warping of time behave as a fourth dimension?

My problem is that I have a hard time grasping something if I can't conceptualize it, though maybe this can not be conceptualized, just accepted, in which case I thank you for your patience. The ...
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4answers
182 views

Expansion of the universe and strain

From cosmological models that involve expansion of the universe, can we not say that there are ever increasing tidal forces felt by solid bodies? If so, the material in solid bodies like metal ...
1
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1answer
123 views

What is the mass in $\vec{\nabla}\cdot \vec{B}_g=\text{something}$ called if it could be non-zero?

Maxwell's equation for gravity has $$\vec{\nabla}\cdot \vec{B}_g~=~0,$$ see Gravitoelectromagnetism in analogy with the electrodynamics. What is the mass called that needs to make these equations ...
9
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1answer
412 views

The Role of Active and Passive Diffeomorphism Invariance in GR

I'd like some clarification regarding the roles of active and passive diffeomorphism invariance in GR between these possibly conflicting sources. 1) Wald writes, after explaining that passive ...
5
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4answers
392 views

Why is space-time four dimensional?

Wikipedia says, "In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional space-time. Momentum is a vector in three dimensions; ...
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2answers
204 views

How do you show from the index notation that the change of frame formula for a metric must involve the transpose?

Let $x^\mu$ and $x^{'\mu}$ be two coordinate systems related by $$dx^{'\mu}~=~S^\mu{}_\nu~ dx^\mu.$$ In index notation the metric in both systems are related by: ...
4
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1answer
112 views

Curvature of spacetime: pincushion distortion?

This may be an elementary question, but if gravity causes a curvature in spacetime, then why isn't everything distorted when looking down on earth, or up at the moon? Shouldn't there be a pincushion ...
2
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2answers
76 views

Question about gravity felt at various radii within a massive sphere

Imagine there's a sphere of radius $R$ which has constant density $\rho$ and you can stand anywhere inside of the sphere. Wherever you stand within the sphere, you'll only feel gravity coming from the ...
7
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1answer
175 views

Book on optics in curved space-time

As evidenced from my earlier questions on vision and curved space, I am struggling a little bit with visual perception in curved space-time. I would like a book recommendation on optics and vision in ...
3
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1answer
83 views

Energy of a black hole : a quizz question

Consider a standard eternal Schwarzschild black hole of mass $M$. One wants to speak about the energy $E$ of a black hole, so let 's present this as a quizz. 1) This is a non-sense to speak about ...
4
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3answers
249 views

Why gauge theories have such a success?

[This question was inspired by a identical question asked on a other forum] Note that we may morally include general relativity in the gauge theories. We may have several (some are deliberately ...
1
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1answer
187 views

Weyl & Riemann curvature tensors and gravitational “physical” quantities in Einstein vacuum equations

If we look at the Einstein vacuum equations, that is without matter (there is the possibility or curvature without matter), for instance we may consider gravitational waves. The question is: Is there ...
0
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2answers
60 views

Expand metric $g_{ij}$ about flat space

I expand metric $g_{ij}$ about flat space $\delta_{ij}$ $$g_{ij}=\delta_{ij}+h_{ij}$$ where $|h_{ij}|\ll 1$. I would like to find $R_{ij}$, to linear order, in terms of $h_{ij}$, but I dont know ...
7
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3answers
320 views

Geometric interpretation of Electromagnetism

For gravity, we have General Relativity, which is a geometric theory for gravitation. Is there a similar analog for Electromagnetism?
3
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1answer
261 views

In general relativity, are light-like curves light-like geodesics?

Just as the title. If a curve is light-like, i.e. a null-curve, is it definitely a null geodesic?
3
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0answers
113 views

Dirac equation in curved space-time with Torsion

I am looking for pedagogical references in which Dirac equation in space-time with curvature and torsion were discussed.
2
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2answers
121 views

What are the relativistic effects of expanding spacetime?

This is a question I've been mulling over for a while and I'm hoping someone here can point me in the right direction. Sorry if it's a bit of a novice question. For the record, I don't fully know GR, ...
13
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1answer
395 views

Current status of Penrose-Hawking “thunderbolts?”

I recently came across the interesting statement that most definitions of cosmic censorship (CC), and most work on proving it, don't exclude something that Hawking calls a "thunderbolt" (Penrose 1978, ...
3
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1answer
112 views

Twist of null Killing fields

I have a (hopefully) quick question: is it possible to have a null Killing field $\xi ^ \mu$ such that the twist 1-form $\omega_{\mu} = \epsilon_{\mu\nu\alpha\beta}\xi^\nu \nabla^\alpha \xi^\beta \neq ...
8
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2answers
470 views

Black hole complementarity - absorption of Hawking radiation

I try to understand two principles formulated by Leonard Susskind in his book The Black Hole War: 1, To any observer who remains outside a black hole, the stretched horizon appears to be a hot layer ...
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2answers
178 views

Second law of thermodynamics implies a linear cosmology?

If one applies the second law of thermodynamics to the Universe[1] as a whole then one might expect that the entropy of the Universe always increases as time goes forward (or more accurately that the ...
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0answers
41 views

Is the space-time deformation only a way to say how gravity works? [duplicate]

Here we have the classical picture of the deformation of the space-time: https://blogs.stsci.edu/livio/files/2012/06/spacetime.jpg And I would to know if this representation is only a way to say how ...
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2answers
279 views

3 Questions about modern Physics [closed]

First i'd like to apologize for both my writting skills (i'm not english) and for my physics knowledge (being them very basic and/or naive). With general relativity from Einstein, gravity is no ...
2
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2answers
377 views

Einstein Equation at the Singularity. Understanding the Dr. Michio Kaku's explanation

I'm trying to understand what Dr. Michio Kaku is exaplaining in this video: http://www.youtube.com/watch?v=hydDhUNvva8 I'm just able to rewrite this two equations. I think I've probably made ​​some ...
4
votes
1answer
131 views

What techniques can be used to prove that a spacetime is not asymptotically flat?

The modern coordinate-indepenent definition of asymptotic flatness was introduced by Geroch in 1972. You can find presentations in Wald 1984 and Townsend 1997. The definition is in terms of existence ...
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1answer
255 views

Projectile motion of a charged particle in a homogeneous electric field

I'm reading an article about projectile motion, but I'm having some trouble with how the author found the equations of motion when a homogeneous electric field is considered. To allow an immediate ...
4
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1answer
146 views

Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
0
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2answers
151 views

How do gravitons impact on general relativity?

As I'm reading about GR a lot lately, I was wondering: how do gravitons (if they exist ofc) impact the general relativity? Since in GR, when we look at particles moving in space-time, we are only ...
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1answer
136 views

Expansion of action in general relativity?

I am reading a lot about GR lately (because of thesis), and one thing bothers me, and I'm not finding a direct answer to it. For instance in one article, the author says that they are expanding ...
1
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1answer
127 views

Does gravitational lensing violate Fermat's Principle that light must travel in straight lines?

Does bending of light due to warping of space violate Fermat's Principle or is it that in the principle light goes in a straight line with respect to space (taking space as the reference) and in ...
10
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9answers
2k views

What is the difference between translation and rotation?

What is the difference between translation and rotation ? If this were a mathematics site, the question would be at best naive. But this is physics site, and the question must be interpreted as a ...
9
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0answers
195 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 ...
13
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1answer
284 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
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0answers
55 views

Motivation behind studying the asymptotic structures

I am trying to explain to myself the motivation behind studying the asymptotic structures at null, time-like and space-like infinities (For the purposes of this post, I will stick to four dimensional ...
5
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0answers
114 views

Questions on Penrose's paper - Conformal Treatment of Infinity

I have several questions. Perhaps it would be better to separate them into different posts. However, given their relative closeness to each other, I think putting it all in one place would be better. ...
6
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2answers
121 views

Why do we care about the maximally extended versions of spacetimes?

One can take a spacetime and maximally extend it, so that geodesics end only on singularities, where they have to end -- not on coordinate singularities, which are not physically significant. But when ...
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1answer
252 views

The Einstein-Klein-Gordon (EKG) equations

I am a little confused about a few papers I read on the Einstein-Klein-Gordon (EKG) equations. From what I understood one takes the energy-stress-tensor of the scalar field: $$T_{\mu\nu } = ...
2
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2answers
84 views

Cosmological models other than FRW

The FRW is a nice isotropic and symmetric metric but I think its assumptions are too many. I was wondering about alternative models. Specifically are there any prominent alternatives that have more ...
3
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1answer
219 views

What does “all future lies within the event horizon” mean?

I was trying to find an answer as to why light does not escape black holes and I stumbled upon this Phys.SE question. In the answer it said that: "Since all future lies within the event horizon, ...
2
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0answers
105 views

On “the geometry of free fall and light propagation” paper by Ehlers

In the paper The geometry of free fall and light propagation by Ehlers and his colleagues (Gen. Relativ. Gravit. 44 no. 6, pp. 1587–1609 (2012)), I reach to an axiom which says: There exists a ...
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0answers
21 views

What is time? Why we relate it to the velocity of light? [duplicate]

what is time? why we relate time to the velocity of light as we already know that light also take some time to travel?
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2answers
254 views

Is the tide on Earth caused by curvature of spacetime

The tide on Earth appears absolutely whenever the moon is overhead. Is that tide caused by spacetime, re-curvature in space or attraction gravity?
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1answer
55 views

Scaling of non-gravitational energy in a black hole

When looking at a Schwarzschild black hole, for instance, we know that we may apply black hole thermodynamics. We may define a entropy of the black hole which scales like the area of the horizon : $$S ...