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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Where did Karl Schwarzschild derived his solution?

Does anyone know more about circumstances of Karl Schwarzschild at the Russian front in 1915 where he allegedly derived his famous solution of the Einstein equations (describing a black hole)? Sources ...
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564 views

Vacuum energy and perpetual motion

The part of the Einstein equations of general relativity referred to vacuum energy, introduce a repulsive term in gravity. This means that as the space become bigger and bigger, vacuum part become ...
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4answers
158 views

How do black holes accrete mass?

Thanks to time dilation, a distant observer watching a man fall in to a black hole will only see him asymptotically approach the event horizon. So how do black holes ever get bigger?
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1k views

Tiling hexagons on a sphere surface

In attemopt to understand basic principles of non-Euclidean geometry and its relation to physical space, I am reading General Relativity by Ben Crowell. On page 149 there is a discussion of hexagons ...
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349 views

Another faster-than-light question

Imagine we have something very heavy (i.e supermassive black hole) and some object that we can throw with 0.999999 speed of light (i.e proton). We are throwing our particle in the direction of hole. ...
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363 views

Kerr geodesics differential equations in equatorial plane

With friend, we are writing an interactive educational simulation of particle falling into a black hole. Currently we use Schwarzschild geodesics. However, we want to generalize it to the case of ...
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628 views

Is spacetime flat inside a spherical shell?

In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
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104 views

What else does the fabric of space-time do?

I know that, the fabric of space is bended so there is a path for another planet to follow to cause gravity I.E. the sun and the earth ( i think) Is htere any othe rthing's the fabric of space-time ...
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228 views

What's the difference between the equivalence principle and curvature of spacetime?

Calculating using the equivalence principle only accounts for half the deflection of light, whereas the other half is from curvature of space-time. But isn't the equivalence principle the same thing ...
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293 views

Extending General Relativity with Kahler Manifolds?

Standard general relativity is based on Riemannian manifolds. However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
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734 views

What bends fabric of space-time?

I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it? Other energy sources, forces ...
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Gravity stronger than electromagnetic force in a black hole?

Well, the question has somewhat been answered before, but there's one part missing, which - I'd think - is in conflict with the physical laws. The earlier reply says that the gravitational pull even ...
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80 views

Ultracold atoms and General theory of Relativty

I am looking for good reviews for the subject of Ultracold atoms and it's application in test of General theory of relativity. I am planning to pick up this topic as a semester project, can somebody ...
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888 views

Metric tensor under coordinate transformation x to y(x)

Say I have a metric representation $g_{\mu\nu}$ in a coordinate system $x$ and I want to find the representation of the metric in a new set of coordinates $y = y(x)$. I know how to do this if you are ...
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150 views

Symmetries of spacetime and objects over it

I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
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112 views

Is there a formula to work out how much the fabric of spacetime bends?

From my knowledge, a big mass (planet star etc) can bend the fabric of spacetime. Is there a formula that we can use to work out how much it bends?
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Are gravitational waves longitudinal or transverse?

Waves are generally classified as either transverse or longitudinal depending on the they way the propagated quantity is oriented with respect to the direction of propagation. Then what is a ...
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427 views

Is the Schwarzschild black hole unphysical?

To obtain the Schwarzschild metric from Einstein equations of general relativity, we suppose that the energy density is a distribution : $$ \rho (\vec{r}) = M \delta(\vec{r})$$ The Schwarzschild ...
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394 views

Causal and Global structure of Penrose Diagrams

What kind of global and causal structures does a Penrose diagram reveal? How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure? Also, I ...
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Why does no physical energy-momentum tensor exist for the gravitational field?

Starting with the Einstein-Hilbert Lagrangian $$ L_{EH} = -\frac{1}{2}(R + 2\Lambda)$$ one can formally calculate a gravitational energy-momentum tensor $$ T_{EH}^{\mu\nu} = -2 \frac{\delta ...
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253 views

Linearized Einstein Equations

I've been trying to prove this equation: $$ \delta ...
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92 views

Is it fabric of space or fabric of space-time?

Very quick question, in the general relativity is it fabric of space, fabric of space-time or both mentioned?
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564 views

Do Christoffel symbols commute?

Do Christoffel symbols commute? For example, does $\Gamma^{e}_{db}\Gamma^{c}_{ea} = \Gamma^{c}_{ea}\Gamma^{e}_{db}$?
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227 views

How many pieces of toast would you need to make a black hole?

I am trying to find the following: How many pieces of toast would you need to make a black hole? From what I've learnt so far I need to find an equation for the compression force the massive amount ...
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677 views

Was the Higgs mass correctly predicted by asymptotic safety of gravity?

This paper was published in Phys Lett B in 2009, and predicted the Higgs mass to be 126 GeV based on the asymptotic safety of gravity. Is this prediction taken seriously by the theory community, or is ...
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659 views

What is the general relativistic calculation of travel time to Proxima Centauri?

It has already been asked here how fast a probe would have to travel to reach Alpha Centauri within 60 years. NASA has done some research into a probe that would take 100 years to make the trip. But ...
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5answers
3k views

Is the total energy of the universe constant?

If total energy is conserved just transformed and never newly created, is there a sum of all energies that is constant? Why is it probably not that easy?
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319 views

Einstein tensor in Friedmann equations : where is the missing $c^2$?

I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere. In all the following $\rho$ ...
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2k views

Killing vector fields

I am facing some problems in understanding what is the importance of a Killing vector field? I will be grateful if anybody provides an answer, or, refer me to some review or books.
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264 views

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 < ...
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132 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 ...
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1answer
210 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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190 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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675 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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2answers
354 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 ...
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313 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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Do intergalactic magnetic fields imply an Open Universe?

According to a recent paper on the arXiv, they do. How credible is this result? The abstract says: The detection of magnetic fields at high redshifts, and in empty intergalactic space, support ...
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424 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
444 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
147 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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191 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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1answer
342 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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1answer
505 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 ...
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1answer
106 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
810 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 ...
6
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1answer
459 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
188 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 ...
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1answer
286 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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2answers
837 views

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
64 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 $. ...