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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Cosmology with a negative cosmological constant

Based on the Friedmann equation for a universe with only cosmological constant, $$\left(\frac{\dot{a}}{a}\right)^2 \sim \Lambda$$ I would expect the scale factor $a(t) \sim e^{-it}$ if $\Lambda < ...
4
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1answer
158 views

Rotation of Spacetime => Change in orbit/path

Along the idea of frame-dragging; Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space? I've seen the fact that depending on the ...
2
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1answer
237 views

Why are black hole singularities stable?

The Friedmann equations says that huge matter densities lead to huge expansion rates. In Newtonian gravity, two massive point particles separated by an infinitesimal distance will experience an ...
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308 views

What is meant by the term “mean rest frame”?

I found this part in the book of Bernard Schutz on GR. (Sec 12.2: General Relativistic Cosmological Models). Robertson-Walker metrics: We shall adopt the following assumptions about the universe: ...
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919 views

If you are carrying a magnet, can you tell when you cross the event horizon of a black hole?

By the no hair theorem, a black hole is completely characterized by it's mass, charge and angular momentum. Therefore dipole and higher pole magnetic fields are completely expelled when a black hole ...
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486 views

How to think of the harmonic oscillator equation in terms of “acceleration = gradient”

This is related to another question I just asked where I learned that the equation of motion of a harmonic oscillator is expressed as: $$\ddot{x}+kx=0$$ What little physics I grasp centers on ...
9
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540 views

What is the status of existing measurements of the speed of gravity?

In replying to a recent question I stated: Gravitational waves have not been yet experimentally observed so as to have their velocity measured. Which after the fact prompted me to try and verify ...
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746 views

Do intergalactic magnetic fields imply an Open Universe?

According to a paper on the arXiv (now published in Phys Rev D), they do. How credible is this result? The abstract says: The detection of magnetic fields at high redshifts, and in empty ...
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554 views

Why are we talking about space curvature as if we know what space is? [closed]

1) Why are we talking about space curvature as if we know what space is? Every question about gravity seems to evoke an answer involving "space curvature" which seems like an undefined placeholder ...
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3answers
640 views

Taking a derivative involving Einstein summation

Suppose I have something like $ f = g_{\mu \nu} x^{\mu} x^{\nu} $, where the Einstein summation convention is implied. Now suppose I want to to take the derivative $ \partial_{\mu}f = \frac{\partial ...
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2answers
173 views

Most suitable metric for the Solar system?

If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable? I thought about using a Schwarzschild metric near each planet, but ...
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326 views

Classical approach to Schwarzschild radius

The Schwarzschild radius from general relativity is given to be $r = \frac{2GM}{c^2}$. One can obtain the same answer using classical calculations. That is, the escape velocity of a particle is ...
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476 views

If a magnetic monopole falls into a schwarzchild black hole, what happens to the magnetic field?

By the no-hair theorem, black holes can only have mass, charge and angular momentum. Does "charge" include "magnetic charge" (such as from a magnetic monopole)? Can black holes have magnetic charge ...
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681 views

When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field?

By the no-hair theorem, black holes are only characterized by mass, charge and angular momentum. If the star is neutral, the black hole will have only mass and angular momentum - and therefore it ...
2
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1answer
110 views

Rotating hoop in Relativity

What does a rotating hoop, with each point moving at a velocity close to the speed of light, appear like with respect from a stationary observers perspective. For example how does the shape of the ...
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2answers
1k views

Metric tensor and its inverse

Is it always allowed to represent the metric tensor $g_{\mu \nu}$ in General Relativity as a $4\times 4$ matrix? If the last one is represented for example with a $4\times 4$ matrix ...
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1answer
654 views

What happens to an embedded magnetic field when a black hole is formed from rotating charged dust?

Black holes have no-hair so there are uniquely specified by a mass, charge and angular momentum. Imagine a cloud of charged rotating dust. There will be a magnetic field associated with the current ...
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1answer
229 views

Light orbiting a massive body [duplicate]

Possible Duplicate: Can a photon be made to orbit a known (or undiscovered theoretical) body? How massive would a black hole have to be for light to orbit it at 1km away from the ...
5
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1answer
399 views

Dimensional reduction and Schwarzschild solution

It is well-known that, given a Killing vector $\xi_\mu$ for a metric, this can be dimensionally reduced. This is exactly the case of the Schwarzschild solution due to the rotational symmetry. This ...
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What is the physical size of a black hole?

Something that's always confused me. How large is a black hole's physical size - not mass? From descriptions, it would seem that the 'singularity' is a single point, but is it really? Say for ...
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1answer
66 views

Is a volumetric rate frame-invariant in general relativity?

Imagine that I have a radioactive material with a long half life. The atoms in this material decay at a certain rate $R$. The rate is the decay constant times the number density $R = \lambda N $. ...
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2answers
406 views

Relationship between Alcubierre drive space-time evolution and speed of gravity

The top rated answer to this question about the Alcubierre drive asserts, "spacetime can dynamically evolve in a way which apparently violates special relativity," but according to the Wikipedia ...
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2answers
2k views

What is the 'apparent horizon' of a black hole?

The Wikipedia article is full of general relativistic and differential geometry jargon, and its accuracy is questionable. So, without such (or explaining said jargon without more jargon), what is the ...
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1answer
148 views

What is the curvature scalar $\Psi_{4}$?

What is the curvature scalar $\Psi_{4}$? Is it related to the scalar curvature $R$? What does its real and imaginary parts represent?
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173 views

How do black holes in merging galaxies find each other to merge?

In many accounts of galaxy mergers, the prompt merging of their central black holes, if any, is stated seemingly as too obvious to need further explanation. While I don't dispute that this may indeed ...
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3k views

Flow of momentum is pressure

In the diagonal terms of the energy-momentum tensor, the flow of $x$-momentum in the $x$-direction is the $x$-pressure. Why the flow of momentum is pressure?
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Will cosmological gravitational waves be weaker or stronger than astrophysical ones?

Will gravitational waves of cosmological origin be weaker or stronger (higher amplitude $h \simeq\Delta L/L$) than those created from astrophysical sources? I'm having a real hard time finding the ...
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1answer
121 views

Are all static solutions of Einstein's equations spherically symmetric?

Is it true that all static solutions in GR are also spherically symmetric? Is there a proof of this? Similarly, are all stationary solutions axisymmetric?
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How did Einstein derive general relativity?

How did Einstein derive general relativity (GR)? Did he use: the equivalence principle? The principle of least action? Anything else? Note, I'm not looking for a full mathematical derivation of GR! ...
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754 views

What is the variation of Gauss-Bonnet term a total derivative of?

What is the variation of Gauss-Bonnet term total derivative of? i.e. Variation of Gauss-Bonnet combination $= \nabla_{\mu} C^{\mu}$. What's $C^{\mu}$ in 4-dimensions?
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307 views

The radius of the universe and time [closed]

Ok - fair warning - Non-physicist asking dumb-assed questions here again. I've been reading a lot of Einstein, Feynmann, Ferris etc. I'm just loving this stuff. But I suddenly found myself looking at ...
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What do you feel when crossing the event horizon?

I have heard the claim over and over that you won't feel anything when crossing the event horizon as the curvature is not very large. But the fundamental fact remains that information cannot pass ...
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Harold White's work on the Alcubierre warp drive

I've read a bit on Harold White's recent work. (A paper on Nasa's site) I haven't been able to find any comments by people claiming to know anything about the physics involved. Is this really serious? ...
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1answer
127 views

Could tidal effects make matter hot enough for nuclear fusion?

There was a recent question about cosmological firewalls. Putting aside questions of entanglement and information and looking at the problem from a pure mechanical viewpoint, we know that although ...
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Implications of Unruh-inertia to theories of gravity

If it turns out to be true that the galaxy rotation curves can be explained away by Unruh modes that become greater than the Hubble scale at accelerations around $10^{-10} m/s^2$ as proposed in here, ...
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1answer
540 views

Einstein's Explanation for gravity vs. Newtonian

I was trying to understand the Einstein's explanation for gravity (gravitational force), and while I am able to understand why two moving masses will be attracted, due to the curving of the space, I ...
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148 views

gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
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1answer
226 views

Where does this equation for a perturbed metric come from?

I'm reading an article which includes the following equation involving a perturbed metric: $$G_{AB} = \eta_{AB} + \overset{1}{\gamma}_{AB} + 2\overset{1}{\chi}_{(A,B)}\tag{4.1}$$ I don't understand ...
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311 views

Can a single particle create a black hole?

Let us suppose a particle with so much energy $ E= h \frac{c}{\lambda} $ so $ \lambda $ is smaller than Planck's length ? Would it be possible? I mean if the particle has so much energy then its mass ...
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Are covariant vectors representable as row vectors and contravariant as column vectors

I would like to know what are the range of validity of the following statement: Covariant vectors are representable as row vectors. Contravariant vectors are representable as column vectors. ...
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136 views

Cosmological relativistic effects : misunderstanding between cosmological and relativistic communities?

I would like to clarify something that mixes cosmology and relativistic effects. Maybe I'm not understanding something or maybe there a difference of vocabulary between the cosmological and the ...
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1answer
121 views

If it is given which intervals are spacelike, can be determined which intervals are lightlike?

Provided that the notion of "$\mbox{spacelike}$"-ness (of an interval) is symmetric: $$\text{spacelike}( \, x - y \, ) \Longleftrightarrow \text{spacelike}( \, y - x \, ),$$ then for any set $X$ (of ...
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1answer
546 views

Space expansion looking like time dilation

Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange before and the ...
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1answer
596 views

Do atoms expand with universe? [duplicate]

Possible Duplicate: Why space expansion affects matter? Why does space expansion not expand matter? As we know, the universe is expanding, galaxies are away from each other. But what ...
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2answers
703 views

Is it possible to have faster-than-light movement in General Relativity?

The speed of light as the maximal possible speed is build into Special Relativity as a premise of the theory. However I know of no such premise in General Relativity. When looking at two stars laying ...
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How much does the curvature of space change the volume of Earth by?

If we assume space is flat the volume of Earth is: $$ V = \frac{4 \pi R^3}{3} = \frac{4 \pi (6378.1 km)^3}{3} = 1.086 \times 10^{21} m^3 $$ The Einstein field equations, however, predict that the ...
6
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2answers
667 views

Linearizing Gravity to ${\cal O}(h^3)$

I've seen the action of linearized gravity in many places. We basically have $${\cal L} ~\sim~ \frac{1}{G_N}\left( - \frac{1}{2}h^{\alpha\beta} \Box h_{\alpha\beta} + \frac{1}{4} h \Box h + {\cal ...
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219 views

Event Horizon fluctuating due to gravitational waves

Do the interiors of black-holes create gravitational waves and if so do these waves cause the radius of the event horizon to fluctuate as the waves pass the horizon ?
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360 views

What does adding a scalar field component to the Einstein field equations mean for black holes and string theory?

If a scalar field component has to be added to the Einstein field equations (see below) to solve dark matter/energy, then how would string theory need to be modified and do black holes still exist? ...
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Is it possible to describe the entire universe with the behavior of an $\mathbb{R}^n$ field?

Suppose every phenomena in this universe (of course most are reducible to some particular general ideal ones - basically I'm talking about those!) could be described as ...