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.
5
votes
2answers
110 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 ...
1
vote
1answer
258 views
warp drive with gravitational waves in the nonlinear regime
gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ...
10
votes
5answers
528 views
Why do we still need to think of gravity as a force?
Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me.
We always hear ...
1
vote
1answer
35 views
How to find distance of closest approach for a Schwarzschild geodesic?
What is the distance of closest approach in this Wikipedia article?
I can't seem to find its definition, and this other question doesn't have an answer I can understand.
3
votes
3answers
44 views
Showing Hubble constant is time-independent
I have the following question for homework:
Show that the Hubble constant $H$ is time-independent in a universe in which the only contribution to energy density comes from vacuum energy.
So in ...
0
votes
1answer
41 views
How does gravity effects both time and light if they have no mass [duplicate]
I've been reading about how black holes can effect both time and light with gravity. So I was wondering, doesn't something have to have mass to be effected by gravity? And if so, does this mean both ...
18
votes
1answer
309 views
+300
Does a charged or rotating black hole change the genus of spacetime?
For a Reissner–Nordström or Kerr black hole there is an analytic continuation through the event horizon and back out. Assuming this is physically meaningful (various site members hereabouts think ...
5
votes
2answers
291 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 ...
0
votes
0answers
21 views
Is a dynamical extension of non-commutative black holes feasible?
Non-commutative (sometimes called "fuzzy") black holes are solutions of Einstein's equations obtained with a previous basic assumption of non-commutativity of the coordinates $[x^{\mu},x^{\nu}]=i\, ...
6
votes
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 – ...
9
votes
8answers
1k views
Is Mach's Principle Wrong?
This question was prompted by another question about a paper by Woodward(not mine). IMO Mach's principle
is very problematic (?wrong) thinking. Mach was obviously influenced by Leibniz. Empty space ...
0
votes
1answer
89 views
can be exist the negative mass? [duplicate]
I'm not sure about this but I guess there must be negative masses in the universe because of the symmetry. If the gravity is one of the main forces in nature it must has negatives mass to be able to ...
0
votes
0answers
83 views
How can it be seen that ST unifies GR and QM as the quantum gravity scale is not directly accessible
I am a newbie to superstring theories, but I came into this question:
so superstring theories purport to unify general relativity and quantum theory.
However, there is yet no definitive way to test ...
1
vote
1answer
28 views
Can we build a synthetic event horizon?
If we imagine ourselves to be a civilization capable of manipulating very heavy masses in arbitrary spatial and momentum configurations (because we have access to large amounts of motive force, for ...
6
votes
4answers
400 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?
4
votes
1answer
89 views
“Redshifting” of forces in stationary space - times
Here's the problem statement:
Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor).
(a) Show that the ...
2
votes
1answer
54 views
Derivation of Weyl tensor
I want to derive the Weyl tensor along the lines of this derivation,
but I am unable to complete it. (I am only interested in $4$ dimension for now.)
Every contraction I perform gives either $0=R + 3 ...
2
votes
1answer
90 views
Energy Functional
I am a graduate student in pure mathematics, during my study on Ricci Flow I faced some functional known as energy functional. For example Einstein-Hilbert functional is called an energy functional, ...
3
votes
1answer
55 views
Some sort of conservation equation
As far as I know, in General Relativity, an expression of the kind
$\nabla_{\mu} X = 0$
states that, associated to $X$, there exist a charge which is conserved.
The first example that comes to mind is ...
2
votes
1answer
122 views
Ricci identity/Riemann curvature tensor and covectors
Can somebody please explain to me how the following statement is true?
The Riemann curvature tensor $R^c_{dab}$ is given by the Ricci identity $$(\nabla_a\nabla_b-\nabla_b\nabla_a)V^c\equiv ...
4
votes
0answers
54 views
Gravitational redshift of Hawking radiation
How can Hawking radiation with a finite (greather than zero) temperature come from the event horizon of a black hole? A redshifted thermal radiation still has Planck spectrum but with the lower ...
1
vote
1answer
81 views
Killing vector argument gone awry?
What has gone wrong with this argument?!
The original question
A space-time such that $$ds^2=-dt^2+t^2dx^2$$
has Killing vectors $(0,1),(-\exp(x),\frac{\exp(x)}{t}), ...
1
vote
1answer
209 views
What is the general relativistic calculation of travel time to Proxima Centauri?
It has already been asked here how fast a probe would have to travel to reach Alpha Centauri within 60 years. NASA has done some research into a probe that would take 100 years to make the trip. But ...
3
votes
2answers
112 views
Geodesic equations
I am having trouble understanding how the following statement (taken from some old notes) is true:
For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$
the timelike geodesics ...
2
votes
1answer
92 views
Stress energy tensor of a perfect fluid and four-velocity
In the following demonstration, there is an error, but I cannot find where. (I explicitely put the $c^2$ to keep track of units).
We consider a metric $g_{\mu\nu}$ with a signature $(-, +, +, +)$ :
...
13
votes
1answer
147 views
Is period of rotation relative?
My question is inspired by the following answer by voix to another problem:
"There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently ...
3
votes
1answer
77 views
The most general form of the metric for a homogeneous, isotropic and static space-time
What is the most general form of the metric for a homogeneous, isotropic and static space-time?
For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
1
vote
1answer
64 views
Assuming space is infinite can our observable universe be an island amongst an archipelego?
According to recent measurements our observable universe is roughly 93 billion light years in diameter; also it appears (according to WMAP measurements) that spacetime is flat.
Supposing space is ...
1
vote
2answers
164 views
Excluding big bang itself, does spacetime have a boundary?
My understanding of big bang cosmology and General Relativity is that both matter and spacetime emerged together (I'm not considering time zero where there was a singularity).
Does this mean that ...
13
votes
2answers
557 views
Symmetrical twin paradox
Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are ...
6
votes
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 ...
1
vote
1answer
86 views
How can the derivative of this trace be constrained?
I am studying for my exam on relativity and I am going through some problems sets including ones where I was not very successful in so I want to know how to do this problem.
(Convergence of ...
0
votes
1answer
44 views
Does the actual curvature of spacetime hold energy?
My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
91
votes
13answers
5k views
How does gravity escape a black hole?
My understanding is that light can not escape from within a black hole (within the event horizon). I've also heard that information cannot propagate faster than the speed of light. It would seem to ...
5
votes
0answers
87 views
Equation of state of cosmic strings and branes
I'm sure these are basic ideas covered in string cosmology or advanced GR, but I've done very little string theory, so I hope you will forgive some elementary questions. I'm just trying to fit some ...
2
votes
0answers
50 views
How to keep the clock of a spaceship synchronised to the clock of an observer? [duplicate]
I read that the clocks of GPS satellites seem to run slower than the clock of stationary observer, because of their speed (special relativity) and seem to run faster than the clock of stationary ...
1
vote
3answers
258 views
Similarity between the Coulomb force and Newton's gravitational force
Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
6
votes
3answers
215 views
Why Can We Observe Space Curvature / Warping At All?
I don't understand why we are able to see and measure curvature / warping of space at all.
Space as I understand it determines distances between objects, so if space were "compressed" or warped, ...
3
votes
0answers
71 views
Curvature and spacetime
Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
1
vote
1answer
60 views
Evaluating the Ricci tensor effectively
If given a metric of the form $$ds^2=\alpha^2(dr^2+r^2d\theta^2)$$ where $\alpha=\alpha(r)$, then can one immediately conclude that $$R_{\theta\theta}=r^2R_{rr}$$ where $R_{ab}$ is the Ricci tensor, ...
2
votes
0answers
301 views
Calculation of the non-Gaussity parameter for primordial cosmological perturbations by the ADM Formalism
Maldacena has used the ADM Formalism in one of his papers (http://arxiv.org/abs/astro-ph/0210603) in computing the the three point correlation function (i.e the non-Gaussianity) parameter for ...
0
votes
2answers
139 views
General Relativity & Kepler's law
According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus.
However,
according to general theory of relativity,
the earth ...
11
votes
4answers
1k views
Is there a maximum possible acceleration?
I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
1
vote
2answers
79 views
Are there problems solvable with Newtonian physics, GR and QM?
First I must let you know that I don't have much understanding of neither GR nor quantum mechanics, and therefore this question.
I've mentally pictured Newtonian physics, GR and quantum mechanics all ...
2
votes
0answers
66 views
Ising Hamiltonian for relativistic particles
An Ising system is described by the simple Hamiltonian:
$$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$
Here the $x_i$ are spins (+1 or -1 in units ...
1
vote
2answers
105 views
Negative potential energy of gravity
Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)?
If so it seems to me that the ...
2
votes
1answer
49 views
Why does the Kruskal diagram extend to all 4 quadrants?
Why is it that the Kruskal diagram is always seen extended to all 4 quadrants when the definitions of the $U,V$ coordinates don't seem to suggest that the coordinates are not defined in, say, the 3rd ...
0
votes
0answers
33 views
metric extension outside the light cone
Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past ...
3
votes
1answer
91 views
When a variation of a tensor is not a tensor?
In a comment about variation of metric tensor it was shown that
$$\delta g_{\mu\nu}=-g_{\mu\rho}g_{\nu\,\sigma}\delta g^{\rho\,\sigma}$$
which is contrary to the usual rule of lowering indeces of a ...
0
votes
1answer
124 views
Christoffel symbol for Schwarzschild metric
I know that the christoffel (second kind) can be defined like this:
$$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
