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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Gravitation and the QFT vacuum

I'm asking this to get yet another lessson in the inability of QFT and GR to cohabit. Many people believe GR must yield to quantization. The question here is as to why the activity of the vacuum ...
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2answers
765 views

When will the Hubble volume coincide with the volume of the observable Universe?

The Hubble volume is the volume that corresponds to objects so far from the Earth that the space between us and them is expanding faster than the speed of light. (I.e. objects outside this volume ...
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1answer
360 views

Using mass of the observable Universe to estimate an energy equivalent

For quite some time now, physicists have been able to estimate the mass of the observable universe. Reportedly it's around $10^{50} \:\mathrm{kg}$. There is also general relativity, which states ...
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1answer
457 views

Does the Big Bang need a cause? [duplicate]

Possible Duplicate: on causality and The Big Bang Theory Asking here in layman's terms.. When theoretical physicsists discuss the origin of our Universe, the wider consensus appears to be ...
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1answer
543 views

$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics? Suppose one wants to simulate the rotation curve $v(r)$ for galaxies ...
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1answer
294 views

Why can't Schwarzschild wormholes exist?

So, I've recently been reading up on Schwarzschild wormholes and I've learned that they cannot exist becuase they violate the 2nd Law of Thermodynamics. What I'm asking is: Why do they violate the ...
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2answers
614 views

argument about fallacy of diff(M) being a gauge group for general relativity

I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity. basically i have these points that in my view are very solid ...
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4answers
632 views

what is the difference between a blackhole and a point particle

Theoretically, What is the difference between a black hole and a point particle of certain nonzero mass. Of-course the former exists while its not clear whether the later exists or not, but both have ...
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5answers
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What does a frame of reference mean in terms of manifolds?

Because of my mathematical background, I've been finding it hard to relate the physics-talk I've been reading, with mathematical objects. In (say special) relativity, we have a Lorentzian manifold, ...
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4answers
683 views

Why should one expect closed timelike curves to be impossible in quantum gravity?

From the Wikipedia article, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the Chronology ...
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4answers
962 views

Detection of the Electric Charge of a Black Hole

By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the ...
8
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1answer
840 views

Open problems in General Relativity [closed]

I would like to know if there are some open mathematical problems in General Relativity, that are important from the point of view of Physics. I mean is there something that still needs to be ...
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2answers
306 views

How is the complexification of spacetime justified?

As always the caveat is that I am a mathematician with very little knowledge of physics. I've started my quest for knowledge in this field, but am very very far from having a good grasp. General ...
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2answers
610 views

Is spacetime simply connected?

As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn. This falls into the ...
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4answers
352 views

Would there be time dilation at the point where two gravitational fields cancel each other out?

My question is very simple, and most likely a stupid one: One observer is at a point in space were the gravitational force form massive bodies (or a single massive body) cancel each-other out. The ...
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2answers
344 views

Cosmic Microwave Background (CMB) and its relation to Inertial Frames

We know that the CMB is isotropic when viewed outside of the spinning and revolving earth. Is it homogeneous? Can we relate the CMB to an inertial frame in the Newtonian sense (in which space and ...
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0answers
265 views

composition of space expansion and movement as a gauge invariance

suppose i have a space-time where we have one point-like object* which we will call movement space probe or $\mathbf{M}_{A}$ for short, and it will be moving with constant velocity $V^A_{\mu}$ in ...
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6answers
424 views

Objects in Physics as a mathematician would see them

I'm a mathematician with hardly any knowledge of physics. Before I start reading volumes of physics books, I have a few questions that have been bugging me and that will help me start reading physics. ...
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2answers
2k views

maximum rotational speed

I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
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2answers
80 views

In a gas of particles, how is the displacement vector related to the number density?

Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector ...
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1answer
212 views

Is there a simple way to define/solve for a null cone for a general spacetime geometry?

I'm wondering if there's any simple way to define and solve for a null cone for a general spacetime geometry in $n+1$ dimensions, given its vertex $p^\mu$. I can't seem to find a simple way to do it ...
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5answers
697 views

How are the comoving coordinates NOT a prefered reference frame?

Physics me this: The equivalence principle has rigorous physical definitions that say, for one, that the laws of physics are the same in all inertial reference frames. This is to say that the ...
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0answers
275 views

Asymptotic Invariants in General Relativity

I was trying to understand Witten's proof of the Positive Energy Theorem in General Relativity by reading the original argument given by Witten. I am comfortable with the overall argument, but I would ...
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5answers
4k views

Why is gravitation force always attractive?

Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time? PS: If the simple answer to this question is that mass makes space-time ...
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1answer
130 views

Notational(?) Question in Whiting's Paper “Mode Stability of the Kerr Black Hole”

I am a math grad student attempting to read Bernard Whiting's paper "Mode Stability of the Kerr Black Hole." If you are in a university network, the paper should be easily found by a google search. At ...
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6answers
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How exactly does time slow down near a black hole?

How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but ...
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2answers
876 views

Why is BTZ black hole asymptotically $AdS_3$?

The metric for the BTZ black hole is $ds^2=-N^2dt^2+N^{-2}dr^2+r^2(N^\phi dt +d\phi)^2$ where $N^2=-M+\frac{r^2}{l^2}+\frac{J^2}{4r^2}$ and $N^\phi=-\frac{J}{2r^2}$. It is often said that BTZ black ...
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309 views

Small change in theta - polar coordinates

I'm reading (I'm trying to read) Schutz's "A first course in general relativity" (1985). On page 126 he mentions that a small change in angle theta in polar coordinates is given by: I can't see why ...
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1answer
176 views

Can space-time be defined by the requirement that the physical laws are simple?

When I was student I was told that time is defined by the requirement that the physical laws are simple. For example, in classical mechanics time can be defined by the requirment that the velocity of ...
2
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1answer
146 views

Does space-time have a projection to time?

I get confused when I see expressions like "the universe is $x$ years old" or "$10^{-2}$ seconds after the big bang" since it seems to me that relativity shows such statements don't have meaning. Is ...
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2answers
294 views

Effect of gravitation on light

Einstein predicted that the gravitational force can act on light. This was verified in one solar eclipse that light from a star near to the sun's disc bent due to Sun's gravity as predicted. Since ...
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4answers
7k views

What did general relativity clarify about Mercury?

I frequently hear that Kepler, using his equations of orbital motion, could predict the orbits of all the planets to a high degree of accuracy -- except Mercury. I've heard that mercury's motion ...
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1answer
418 views

Does gravitation of a sphere equal gravitation of a point?

Under Newtonian model of gravity, a perfect sphere creates the same gravitation field as a point mass in its center. General Relativity describes gravitation differently. How much this difference ...
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3answers
894 views

Does gravity require strings?

OK, before I ask my question, let me frame it with a few (uncontroversial?) statements: The low-field-limit plane-wave solution to Einstein's equations is helicity-2. In the early days of string ...
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1answer
277 views

Calculating position in space assuming general relativity

Suppose two pointed masses are given in space. Suppose further that one of the masses has a given velocity at (local) time 0. Is there a way to compute its position in a future time? Neglecting ...
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1answer
767 views

2nd order variation of Hilbert-Einstein action + Gibbons-Hawking-York boundary term

While the first order metric variation of Hilbert-Einstein action plus Gibbons-Hawking-York boundary term is well-known and takes the form: $\delta S_{HE}+\delta S_{GHY}=-\frac{1}{16\pi G}\int d^3x ...
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3answers
270 views

What is meant when it is said that the universe is homogeneous and isotropic?

It is sometimes said that the universe is homogeneous and isotropic. What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise ...
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1answer
468 views

Length contraction in rotating frame?

If an observer were to rotate around a point at near light speeds, what sort of length contraction would he observe the universe undergo?
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1answer
191 views

If you removed every particle from space…? [closed]

I'm trying to find something Einstein (I think) said about time...It was something like.. "If you removed every particle from space and were left with only one pocket watch (clock, timepiece?), time ...
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1answer
3k views

Explicit Variation of Gibbons-Hawking-York Boundary Term

Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of ...
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2answers
278 views

How can one reconcile the temperature of a black hole with asymptotic flatness?

A stationary observer very close to the horizon of a black hole is immersed in a thermal bath of temperature that diverges as the horizon is approached. $$T^{-1} = 4\pi \sqrt{2M(r-2M)}$$ The ...
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2answers
2k views

What experimental proof has been found of Einstein's theory?

As a casual science reader, I've always found the implications of relativity (inconsistent clocks after near-light-speed travel and various space-time paradoxes) to be confusing and magical-sounding. ...
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1answer
362 views

A question on an assumption of space-time

"A four-dimensional differentiable (Hausdorff and paracompact) manifold $M$ will be called a space time if it possesses a pseudo-Riemannian metric of hyperbolic normal signature $(+,-,-,-)$ and a ...
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5answers
2k views

Conservation law of energy and Big Bang?

Did the law of conservation of energy apply to the earliest moments of the Big Bang? If so, what theoretical physics supports this? I hear that Einstein's theory of relativity disputes the law of ...
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2answers
217 views

a question about singularities in gravity and Physics in general

I had this doubt bugging my mind for a long time about singularities in Physics. I heard that R.Penrose and S.Hawking have proposed that there could be singularities at Blackholes and at the time of ...
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2answers
207 views

Question about gravity probe B

I have a question about the gravity probe B experiment. According to this site: http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/ The measurements they made confirm Einsteins ...
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2answers
260 views

Would dark matter absorb gravitational waves?

Would the vast and seemingly diffuse clouds of dark matter floating around our galaxy (and most others) absorb gravitational waves? Is this perhaps why we haven't detected any yet?
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3answers
2k views

Gravitational time dilation at the earth's center

I would like to know what happens with time dilation (relative to surface) at earth's center . There is a way to calculate it? Is time going faster at center of earth? I've made other questions ...
3
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3answers
298 views

Singularity-free stationary electro-vacuum solution

Let's say we have a spherically symmetric fluid: $$ T^{\alpha \beta} = \begin{bmatrix} \rho & 0 & 0 & 0 \\ 0 & p & 0 & 0 \\ 0 & 0 & p & 0 \\ 0 ...
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2answers
440 views

Brans-Dicke gravity and Black-Hole “vacuum”

The field equations of the Brans-Dicke gravity are $$\Box\phi = \frac{8\pi}{3+2\omega}T$$ $$G_{ab} = \frac{8\pi}{\phi}T_{ab}+\frac{\omega}{\phi^2} ...