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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Second Law of Black Hole Thermodynamics

I've been looking for a satisfying proof of this, and can't quite find it. I read the brief proof of the black hole area theorem in Wald, which is similar, but doesn't quite come down to the actual ...
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1answer
432 views

How does (or can) SR/GR extend to phase space or symplectic manifolds?

I'm asking this question because of an article in New Scientist about a recent preprint by a group including Lee Smolin. I haven't taken the time to comprehend the paper completely. My knowledge of ...
6
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2answers
395 views

Does rotational energy have effect on gravity/metric?

Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$. Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall ...
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3answers
463 views

Getting back out of an Alcubierre warp bubble

Does the theory on paper provide a way for hypothetical travelers to get back out of the bubble that has gotten them close to their distant destination by compressing all the space in front of them ...
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4answers
874 views

Einstein's “happiest thought”

Einstein described his discovery of the equivalence principle as the "happiest thought of my life". Why? What, in broad conceptual terms, is the logical chain of reasoning that leads from the ...
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2answers
363 views

Can the distance of a quasar be determined accurately?

As noted in A doubt about the age of the universe, the wiki about quasars still contains the following misleading sentence: "The highest redshift quasar known (as of June 2011) is ULAS_J1120+0641, ...
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307 views

evidence on the equation of state for dark energy?

If dark energy contributes mass-energy density $\rho$ and pressure $p$ to the stress-energy tensor, then you can define $w=p/\rho$, where $w=-1$ gives a cosmological constant, $w<-1$ gives a big ...
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3answers
662 views

Vacuum and repulsive gravity

How can one show from General Relativity that gravity is attractive force, and under which conditions it becomes repulsive, also why positive energy vacuum drives repulsive gravity?
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404 views

Which Friedmann equation is redundant?

For flat FLRW cosmology, we can write down two Friedman equations and one matter equation: (1) $H^2=\frac{8 \pi G}{3} \rho$ (2) $\frac{\ddot{a}}{a} = -\frac{4 \pi G}{3} (\rho +3p)$ (3) $\dot{\rho} ...
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133 views

Time dilation and dimensional compactification

Is time dilation a form of dimensional compactification? As a probe approaches a black hole, toward a point on the equator of the event horizon, does general relativity predict that the time ...
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2answers
296 views

Physical Interpretation of a Scalar Quantity Related to Currents/Conservation Laws

Let $Q_{ab} = (\psi_{;a})(\psi_{;b}) - (1/2)g_{ab}|\nabla \psi|^2$ be the energy-momentum tensor of the wave equation in some space time. I will use semicolons to refer to covariant differentiation ...
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270 views

What does scalar phi represent in spacetime?

Trying to understand one-forms and vectors via Schutz's A First Course In General Relativity. His example uses a spacetime diagram, a scalar field phi, a curve (worldline) parametrized using proper ...
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292 views

Charged particle close to a charged black hole - what happens?

Let's assume the Reissner–Nordström metric (charged black hole, non-rotating), for simplicity. The black hole is charged with a powerful electric charge. There's a particle nearby, of non-zero mass, ...
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0answers
271 views

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
736 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
343 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
436 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
524 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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281 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
580 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 ...
3
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4answers
590 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
1k views

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
609 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
884 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 ...
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1answer
784 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 ...
3
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2answers
296 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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575 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
341 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
334 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
263 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
421 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
78 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
203 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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676 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
271 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
3k views

Why is gravitation force always attractive?

Why is the gravitation force always attractive? Is there a way to explain this other than the curvature of space time? PS: If the simple answer to this question is that mass makes space-time curve ...
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1answer
127 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
17k views

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 ...
6
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2answers
827 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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297 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
175 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
145 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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292 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
5k 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
416 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
840 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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271 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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730 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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250 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 ...