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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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 ...
7
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4answers
613 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 ...
2
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2answers
577 views

How are the Weyl & Riemann curvature tensors related to the stress energy tensor in GR?

Einstein's vacuum equations, that is without matter, allows the possibility of curvature without matter. For instance, we may consider gravitational waves. The question is: Is there some link ...
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2answers
73 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 ...
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1k 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?
8
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1answer
791 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?
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237 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
352 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, ...
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1answer
552 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
174 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 ...
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2answers
580 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
329 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
54 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
624 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
970 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 ...
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1answer
421 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
414 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
378 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 ...
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2answers
730 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
328 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 ...
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1answer
228 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 ...
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9answers
7k 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 ...
18
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0answers
761 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
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 ...
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0answers
80 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 ...
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0answers
310 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. ...
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2answers
297 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
592 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 } = −\...
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2answers
101 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
433 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, ...
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0answers
162 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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3answers
940 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
69 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 ...
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1answer
753 views

Induced metric on a null hypersurface

Consider a metric $g_{\mu\nu}(x)$ and a hyper surface ${\cal H}$ defined by $~f(x) = c$. One (or at least I) usually finds the "induced metric" on ${\cal H}$ by solving$~f(x) = c$ for one of the ...
3
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1answer
374 views

Massless fields in curved spacetimes

I read the following statement in one of Penrose's paper zero rest-mass field equations can, with suitable interpretations, be regarded as being conformally invariant. I take this to imply that ...
5
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4answers
2k views

Degrees of freedom of the graviton versus classical degrees of freedom

I have a puzzle I can not even understand. A graviton is generally understood in $D$ dimensions as a field with some independent components or degrees of freedom (DOF), from a traceless symmetric ...
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1answer
171 views

How is a wormhole formed by spacetime surgery?

How is a wormhole formed by performing surgery on spacetime?
3
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1answer
300 views

What are Einstein evolution equations?

In my studies I faced "Einstein evolution equations". I know about "Einstein equation", but I don't know what are "Einstein evolution equations"? Unfortunately, my searches did not result in much. Can ...
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3answers
451 views

A thought experiment on vision and curved spacetime

What follows is a long self-made example to deal with my conceptual issues of visualizing curved spacetime. Imagine an observer floating somewhere in space. He feels no strain on his body, ...
2
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1answer
99 views

Information escape from a black hole

Is the following a possible scenario? If not, why not? Assume there is a supermassive black hole $Z$ isolated in inter-galactic space. Nearby and stationary relative to $Z$ is observer $A$. A number ...
8
votes
1answer
342 views

How does one get these definitions of the energy momentum tensor?

I was just reading a book - Mirror Symmetry by Clay Mathematics Institute, and on Page 402 of the book, the writer says that energy momentum tensor is defined classically by $$\delta S = -\frac{1}{4 \...
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0answers
43 views

Resource for nonphysicists about QM/GR incompatibility [duplicate]

I don't know how to explain the issues at hand in a way that nonphysicists are certain to understand. Can anyone point me to some resource (book, video, it doesn't really matter) that will help me?
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2answers
412 views

Newtonian gravity from the holographic principle?

Can one understand Newton's law of gravitation using the holographic principle (or does such reasoning just amount to dimensional analysis)? Following an argument similar to one given by Erik ...
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1answer
189 views

Dimension & non - locality problem in string theory

I have some questions with string theory: Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
6
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1answer
210 views

Resultant curvature tensor from the Casimir Effect

I've often seen the Casimir effect cited as a source of negative energy/exotic matter with regards to ideas like the Alcubierre drive. The articles then go on to note that the energy required by the ...
0
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1answer
296 views

Metric tensor in General Relativity or otherwise [closed]

What is the metric tensor? How can this be a covariant and contravariant tensor, or a mixed tensor, by raising and lowering indices? How it relates to distance function (metric) and angles? How does ...
3
votes
1answer
464 views

Fulvio Melia's linear Universe

I would be interested in what people think of Fulvio Melia's argument for a linearly expanding Universe. I realize that the experimental evidence seems to be pointing to an accelerating Universe but ...
6
votes
2answers
332 views

Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
0
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1answer
111 views

Is the fraction of radioactive isotopes on the near side of the moon higher than on the far side?

As time passes more slowly in a region of space close to the source of a gravitational field, shouldn't the moon, which always has one side facing towards the earth, have a higher fraction of ...
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1answer
74 views

Newtonian approximation in cosmology

In Peeble's "Large scale structure of the Universe" the Newtonian approximation in cosmology is examined by looking at a transformation that makes the metric locally Minkowski. On pg 38 it is stated ...