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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Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This ...
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2answers
213 views
What happens to orbits at small radii in general relativity?
I know that (most) elliptic orbits precess due to the math of general relativity, like this:
source: http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity
I also know that something ...
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4answers
399 views
Can general relativity be completely described as a field in a flat space?
Can general relativity be completely described as a field in a flat space? Can it be done already now or requires advances in quantum gravity?
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3answers
703 views
Alcubierre Drive - Clarification on relativistic effects
On the Wikipedia article on the Alcubierre drive, it says:
Since the ship is not moving within this bubble, but carried along as the region itself moves, conventional relativistic effects such as ...
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2answers
247 views
What is the weight equation through general relativity?
The gravitational force on your body, called your weight, pushes you down onto the floor.
$$W=mg$$
So, what is the weight equation through general relativity?
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2answers
555 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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2answers
355 views
How can a point-like particle “feel” gravity, if locally the curvature of spacetime is always flat?
I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that
Locally, as expressed in the ...
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3answers
285 views
What is the capture cross-section of a black hole region for ultra-relativistic particles?
What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is
$$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$
for a Schwarzschild BH in the geometric ...
6
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1answer
159 views
Can a deformable object “swim” in curved space-time? [duplicate]
Possible Duplicate:
Swimming in Spacetime - apparent conserved quantity violation
It is well known that a deformable object can perform a finite rotation in space by performing deformations ...
6
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1answer
532 views
What is the stress energy tensor?
I'm trying to understand the Einstein Field equation equipped only with training in Riemannian geometry. My question is very simple although I cant extract the answer from the wikipedia page:
Is the ...
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3answers
338 views
Charging a black hole?
What would happen if we have a black hole and we start shooting at it a single electron at a time, and go on doing it forever? Would the electrons start to bounce off eventually?
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2answers
744 views
What does it mean that the universe is “infinite”?
This question is about cosmology and general relativity.
I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read ...
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5answers
465 views
General relativity and the microscopic/macroscopic distinction
Here is Wikipedia's diagram of the stress-energy tensor in general relativity:
I notice that all of its elements are what would be termed "macroscopic" quantities in thermodynamics. That is, in ...
6
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2answers
277 views
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
$$ T_{EH}^{\mu\nu} = -2 \frac{\delta ...
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2answers
246 views
How can one reconcile the temperature of a black hole with asymptotic flatness?
A stationary observer very close to the horizon of a black hole is immersed in a thermal bath of temperature that diverges as the horizon is approached. $$T^{-1} = 4\pi \sqrt{2M(r-2M)}$$ The ...
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1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
6
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1answer
116 views
Einstein's equations as a Dirichlet boundary problem
Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem?
I am thinking of something along those lines:
Consider a compact manifold $M$ ...
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2answers
255 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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3answers
240 views
How can you tell if a critical energy density is actually a black hole?
Here's a question inspired by Edward's answer to this question.
It's my understanding that the average energy density of a black hole in its rest frame is $\rho_\text{BH}(A)$, a function of surface ...
6
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1answer
273 views
Diffeomorphisms and boundary conditions
I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper.
I found this ...
6
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1answer
207 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
200 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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2answers
35 views
Charged black holes in equilibrium
Consider a pair of (possibly rotating) charged black holes with masses m1, m2 and like charges q1, q2. It seems that under certain conditions gravitational attraction should exactly cancel ...
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1answer
62 views
does the background spacetime of a black hole affects its thermodynamic properties?
The question is this: will the thermodynamic properties of a black hole (Hawking radiation spectra and temperature, entropy, area, etc.) depend if the black hole sits in a DeSitter or an Anti-DeSitter ...
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2answers
310 views
Have red shifted photons lost energy and where did it go?
I think the title says it. Did expansion of the universe steal the energy somehow?
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1answer
534 views
Open problems in General Relativity
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
925 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
171 views
What is the definition of a timelike and spacelike singularity?
What is the definition of a timelike and spacelike singularity?
Trying to find, but haven't yet, what the definitions are.
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1answer
102 views
Why is $R^2$ gravity not unitary?
I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity?
My naive ...
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2answers
162 views
Is the speed of sound almost as high as the speed of light in neutron stars?
Have you ever wondered about the elastic properties of neutron stars?
Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
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2answers
184 views
Black hole collision and the event horizon
Will the event horizons of a two black holes be perturbed or bent before a collision? What will the shape of the event horizon appear to be immediately after first contact?
6
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2answers
153 views
How do the LASERs in LIGO realize that space has expanded as a gravitational wave passes by?
I read an article on LIGO, and I heard it mentioned that it is a nontrivial argument to say that the effect can be measured by interferometry. What happens to space as the wave passes? Does the light ...
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3answers
293 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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1answer
367 views
Wick rotation and the arrow of time
It is well known that we can switch from a statistical system to a quantum mechanical system by a Wick rotation. Has this rotation some implication on the way the time flow? namely, this is an ...
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1answer
400 views
Low frequency electromagnetic waves in General Relativity
I am becoming familiar with the Geometric Optics approximation in General Relativity which (to summarise) says that EM waves follow null geodesics under the geometric optics approximation. In the ...
6
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1answer
136 views
Our Universe Can't be Looped? [duplicate]
With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
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0answers
140 views
Does local physics depend on global topology?
Motivating Example
In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology ...
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3answers
165 views
why nontrivially space-like connected event horizons do not respect unitarity?
I want to understand the assertion that the gluing between distant event horizons is forbidden by unitarity. What is exactly the argument that unitarity will necessarily forbid topological nontrivial ...
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1answer
282 views
Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?
The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
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4answers
658 views
Is there a fundamental reason why gravitational mass is the same as inertial mass?
The principle of equivalence - that, locally, you can't distinguish between a uniform gravitational field and a noninertial frame accelerating in the sense opposite to the gravitational field - is ...
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2answers
439 views
Does perturbation theory break down for quantum gravity?
Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values ...
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9answers
1k views
Is Einstein's 1916 General Relativity paper a recommended way to start learning about the subject?
If a person has a good grounding in classical mechanics, electrodynamics and special relativity, is Einstein's 1916 paper a recommended way of learning about the subject?
After looking through it ...
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2answers
223 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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5answers
2k views
How do I calculate the perturbations to the metric determinant?
I am trying to calculate sqrt(-g) in terms of a background metric and metric perturbations, to second order in the perturbations. I know how to expand tensors that depend on the metric, but I don't ...
5
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4answers
300 views
What is the “foamy space” hypothesis that has been debunked recently?
In "Space-Time Is Smooth, Not Foamy", a Space.com article, it is stated:
In his general theory of relativity, Einstein described space-time as fundamentally smooth, warping only under the strain ...
5
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2answers
259 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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2answers
308 views
What is the likelihood of ever discovering the graviton?
How would one look for and confirm existence of a graviton?
Someone was speaking to me about perhaps one day discovering the graviton, but to me it seems unlikely, although I'm young and essentially ...
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2answers
401 views
Why do objects follow geodesics in spacetime?
Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation ...
5
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2answers
102 views
Einstein Field Equations in other space-time dimensions than 3+1?
This question is apparently quite simple but I can't seem to find an answer to it, so I was hopping anyone could clarify me.
Are the Einstein field equations (EFE) only valid for a 3+1 dimensional ...
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4answers
547 views
How did “no prior geometry” father 50 years of confusion?
I've come across this quote attributed to Misner and Thorne from their book, Gravitation:
'Mathematics was not sufficiently refined in 1917 to cleave apart the demands for "no prior geometry" and for ...
