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.
2
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0answers
123 views
Using the area element in derivation of geodesic
In the derivation of the geodesic, one starts with the integral of the line element (arclength):
$$L(C)=\int_{\tau_1}^{\tau_2}d\tau\sqrt{g_{\mu \nu}\dot{x}^{\mu} \dot{x}^{\nu}}$$
The integrand is ...
4
votes
2answers
138 views
Plausible explanations for 3 local space dimensions
Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons).
One such of course ...
1
vote
2answers
139 views
Projective Transformations in GR
A Thought Experiment:
We are in flat spaceime provided with a reference frame—a rectangular Cartesian frame. The coordinate labels[the spatial labels] are visible to us. Each spatial point is ...
1
vote
1answer
153 views
Proper distance and embedding diagrams?
I'm trying to understand proper distance equation in Schwarzschild spacetime.
$d\sigma=\frac{dr}{\left(1-\frac{R_{S}}{r}\right)^{1/2}}$.
I'm sure I'm missing something really obvious here, but how ...
2
votes
1answer
253 views
Difference between coordinate and proper distance in Schwarzschild geometry
I'm trying to understand the difference between proper distance $d\sigma$ and coordinate distance $dr$ in Schwarzschild geometry. The bottom bit of the diagram represents flat space, the upper bit ...
3
votes
2answers
498 views
Value of the Hubble constant over time
There is something I don't understand about the Hubble "constant" H, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have
V = D * H
which means ...
1
vote
0answers
174 views
The structure of space-time
I came across this paper recently called The Small Scale Structure of Spacetime and the following idea occured to me:
To uninformed humans the universe appears Euclidean but we know from GR that on a ...
2
votes
1answer
212 views
Vanishing Ricci flow on a curved manifold
If I understand this right the Ricci flow on a compact manifold given by
$\partial g_{\mu \nu} = - 2R_{\mu \nu} + \frac{2}{n}\!R_{\alpha}^{\alpha} \,g_{\mu \nu}$
tends to expand negatively curved ...
2
votes
2answers
164 views
Can the implications of dark energy be used to bridge the gap between Quantum Mechanics and General Relativity?
Can the findings of the Physics Nobel Laureates of 2011, namely the overpowering existence of dark energy (vacuum energy) have any implications in the quest the combine Quantum Mechanics and General ...
-1
votes
1answer
130 views
Law of conservation of energy at the space.? [closed]
Energy can neither be created nor be destroyed,
if energy disappear in one form it will reappear in another form without any loss.
so what will happen if FAN switched on in the space. ?
1.Electrical ...
1
vote
2answers
197 views
Is it necessary to embed a 4D surface in 5D space?
Lets consider the line element:
$$ds^2=dr^2+r^2[d\theta^2+\sin^2\theta d\phi^2]$$
There are three variables r,theta and phi.
If we use a surface constraint like r=constant the number of
independent ...
3
votes
2answers
352 views
This Expansion-of-the-Universe-Diagram Confuses Me
The following blue-cone Wikipedia diagram confuses me.
At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed ...
4
votes
4answers
835 views
That 10km/day error predicted if GPS satellite clocks not corrected for relativity
Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite ...
1
vote
2answers
176 views
curvature tensor component capable of doing work on $T_{\mu \nu}$
I'm wondering what part of the curvature tensor is able to do work (and hence transfer energy) in matter. I'm wondering if this tensor: http://en.wikipedia.org/wiki/Stress-energy-momentum_pseudotensor ...
4
votes
1answer
448 views
Lagrangian for Relativistic Dust derivation questions
In most GR textbooks, one derives the stress energy tensor for relativistic dust:
$$
T_{\mu\nu} = \rho v_\mu v_\nu
$$
And then one puts this on the right hand side of the Einstein's equations. I ...
3
votes
3answers
574 views
Action principle for the Electromagnetism and Gravity
Here is the formula for the stress energy tensor:
$$
T_{\mu\nu} = - {2\over\sqrt{ |\det g| }}{\delta S_{EM}\over
\delta g^{\mu\nu}}
$$
(This follows from varying the total action $S ...
2
votes
1answer
128 views
Dark matter and mass-energy conservation
I have been thinking recently about dark matter, and it lead me to the following question.
Consider a hypothetical particle which, like the photon, is chargless and massless. However, unlike the ...
2
votes
2answers
1k views
What is the affine parameter for null geodesic?
For time-like geodesic, the affine parameter is the proper time $\tau$ or its linear transform, and the geodesic equation is
...
6
votes
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 ...
6
votes
4answers
259 views
Velocity Time Dilation
In Wikipedia article about time dilation, it says:
"Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners...the moving clocks were expected ...
1
vote
1answer
116 views
Violation of Lorentz symmetry on cosmological distances
This question is about the domain of validity of Lorentz symmetry.
As far as I know, general relativity is a generalization of special relativity. Does that mean that Lorentz symmetry is violated on ...
7
votes
2answers
459 views
Does a Weak Energy Condition Violation Typically Lead to Causality Violation?
In the answer to this question: ergosphere treadmills Lubos Motl suggested a straightforward argument, based on the special theory of relativity, to argue that light passing through a strong ...
6
votes
3answers
130 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
3
votes
2answers
273 views
ergosphere treadmills
suppose you place a number of rotating black holes in linear sequence (rotating around the same axis) between two stars at distance $d$ (assume as tightly packed as practical for purposes of ...
1
vote
1answer
126 views
On BE and FD Statistics
Lets consider the Bose-Einstein and Fermi-Dirac statistics:
Bose-Einstein statistics:
$$\langle n_i\rangle = \frac{1}{\exp{[(\epsilon_i-\mu)/kT]} - 1}$$
Fermi-Dirac statistics:
$$\langle ...
-3
votes
2answers
230 views
Local Charts in General Relativity
We may consider a "local" region in curved spacetime (local in respect of the spatial and the temporal coordinates). A "local inertial frame" may be constructed by some transformation that produces ...
2
votes
2answers
287 views
Theoretical basis for black hole evaporation
What is the basis for black hole evaporation?
I understand that Hawking-radiation is emitted at the event horizon, a theoretical result originating in General Relativity and Quantum Field Theory, but ...
2
votes
1answer
171 views
Laws of physics and general relativity
I'm reading that general relativity let's us describe physics from the point of view of both inertial and accelerated observers. What does that actually mean in terms of doing actual physics? For ...
1
vote
3answers
702 views
Inertial frames of reference
I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it.
I've read ...
4
votes
3answers
253 views
Is the equivalence principle strictly fulfilled by general relativity?
The equivalence principle states
The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
Any real local ...
1
vote
2answers
396 views
Is 4-velocity normalized to -1 even for non-geodesic timelike curves?
In Hartle's General Relativity book ("Gravity"), one of the problems (chapter 8 problem 6) is to prove that $g_{\mu\nu}u^\mu u^\nu$ is conserved along geodesics (really not hard to show), where ...
0
votes
0answers
89 views
Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]
Similar to this reference, are there more such references / works [including textbooks] available in the literature?
(A list would be greatly welcomed and appreciated.)
With great appreciation.
2
votes
0answers
113 views
Intuitively, what is the source term of the Einstein field equation? [duplicate]
My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
2
votes
2answers
483 views
Galilean transformation in relativity
Assume flat spacetime in a general relativistic framework (or special relativity for that matter) and two observers $A$ and $B$, with non-vanishing velocity relative to each other. We know that they ...
2
votes
1answer
165 views
What determine whether the dynamical equations are tensor equations or vector equations?
Newton's 2nd law which is central to Newtonian dynamics, is a vector equation
$\sum\textbf{F}_{external}=m\textbf{a}$
Same with Maxwell's equations in the covariant form.
On the other hand, ...
4
votes
2answers
454 views
Critics of Mannheim's Conformal Gravity Theory?
I'm looking for more articles/reactions/critiques/support for Philip Mannheim's recent conformal gravity theory.
See here: http://arxiv.org/abs/1101.2186v1
Any ideas on where to start?
4
votes
0answers
25 views
What is the state-of-the-art on spacelike singularities in string theory?
What lessons do we have from string theory regarding the fate of singularities in general relativity?
What happens to black hole singularities? What happens to cosmological singularities?
Which ...
10
votes
3answers
3k views
Why you need a graviton when you have the higgs boson?
Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now)
"Why you need a gauge boson for gravity when the higgs ...
1
vote
1answer
145 views
How do we resolve a flat spacetime and the cosmological principle?
As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the cosmological ...
1
vote
1answer
150 views
Can a super-extremal charged black hole be made out of electrons only?
In a previous Question it was argued that it would be impossible to add enough charge to a black hole to make it pass the extremal black hole limit since adding charge would increase the mass of the ...
7
votes
4answers
379 views
How does the star that has collapsed to form a Schwarschild black hole appear to an observer falling into the black hole?
I understand that to an outside observer, the light from a star that is collapsing into a black hole will become more and more red-shifted as the surface of the star appears to approach the black hole ...
2
votes
3answers
406 views
Defining a Riemannian manifold - made easy?
In the context of GTR spacetime, I'm trying to get the basic idea of a Riemannian manifold clear in my mind. Apologies for the longwindedness.
Question 1. Is this a reasonable, simplified summary of ...
6
votes
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 ...
3
votes
1answer
177 views
Could a ship equipped with Alcubierre drive theoretically escape from a black hole?
Also could it reach parts of the universe that are receding faster than the speed of light from us?
4
votes
2answers
369 views
Can an “absolute” frame of reference be determined by measuring the compression of light?
General relativity tells us that there is no absolute frame of reference (actually, it tells us that all frames are relative, which is close but not the same as there is no absolute frame).
Special ...
3
votes
2answers
239 views
Pressure Inside an Ideal Gas
A non-relativistic ideal gas exerts a pressure at the surface of its container
$p = \frac13 \rho \langle v^2 \rangle$
where $\rho$ is the mass density of the gas and $\langle v^2 \rangle$ is the ...
3
votes
2answers
310 views
Black hole complementarity
Black hole complementarity states that two observers, one falling into a black hole, and one observing outside, experience two different histories but since they can not communicate there is no ...
4
votes
1answer
304 views
How does an object falling into a plain Schwarschild black hole appear from near the black hole?
I know that when viewed from infinity (or from a very large distance from the black hole event horizon), an object that falls into the black hole will appear to slow down and will become more and more ...
13
votes
1answer
181 views
Sympletic structure of General Relativity
Inspired by physics.SE: http://physics.stackexchange.com/questions/15571/does-the-dimensionality-of-phase-space-go-up-as-the-universe-expands/15613
It made me wonder about symplectic structures in ...
20
votes
2answers
83 views
experimental bounds on spacetime torsion
Did Gravity Probe B provide any bounds on Einstein-Cartan torsion? is a non-zero torsion value at odds with the results regarding frame-dragging and geodetic effects?
