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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73 views
Einstein +Maxwell 's tensor
Why is it true that we can deduce that Einstein's GR equations coupled with Maxwell's EM equations may be written in the form $$R_{ij}=C(F_{ik}F_j^{\,\,k}-{1\over 4}g_{ij}F_{mn}F^{mn})$$
without ...
1
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1answer
232 views
A question on an assumption of space-time
"A four-dimensional differentiable (Hausdorff and paracompact) manifold $M$ will be called a space time if it possesses a pseudo-Riemannian metric of hyperbolic normal signature $(+,-,-,-)$ and a ...
0
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2answers
214 views
Are the intersections of past and future light cones spacelike?
Given a timelike reference worldline (not necessarily geodesic), we can define light-cone coordinates $\tau^+$ and $\tau^-$ so that the 3-D hypersurfaces of constant $\tau^+$ are past light cones of ...
0
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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.
11
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1answer
485 views
Why is there no dynamics in 3D general relativity?
I heard a couple of times that there is no dynamics in 3D (2+1) GR, that it's something like a topological theory. I got the argument in the 2D case (the metric is conformally flat, Einstein equations ...
12
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5answers
710 views
What is a good mathematical description of the Non-renormalizability of gravity?
By now everybody knows that gravity is non-renormalizable, what is often lacking is a simplified mathematical description of what that means. Can anybody provide such a description?
14
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4answers
1k views
How do you calculate the anomalous precession of Mercury?
One of the three classic tests of general relativity is the calculation of the precession of the perihelion of Mercury's orbit.
This precession rate had been precisely measured using data collected ...
8
votes
5answers
575 views
How does the string worldsheet affect the space-time in which they live?
I don't understand much about string theory and never really got much further past the Nambu-Goto action and very basic supersymmetry (SUSY) lectures in my undergraduate courses, but the only thing ...
16
votes
3answers
529 views
Is there a thought experiment which brings to light the contradiction between General Relativity and Quantum Mechanics?
I've been told that GR and QM are not compatible, is there an intuitive reason/thought experiment which demonstrates the issue? (Or one of the issues?)
12
votes
3answers
531 views
If I fall into an evaporating black hole, where do I end up?
This question has been bothering me for a while. I have a crude hypothesis...
As I understand it, an observer falling into a black hole will cross the event horizon at some specific future (proper) ...
10
votes
0answers
275 views
A dictionary of string - standard physics correspondences
Motivated by the (for me very useful) remark
''Standard model generations in string theory are the Euler number of
the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3
...
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 ...
10
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3answers
360 views
Why is there a flux of radiation in the Hawking effect but not in the Unruh effect? (and other questions)
This question is slightly related to this one Do all massive bodies emit Hawking radiation?, which I think was poorly posed and so didn't get very useful answers. There are several questions in this ...
9
votes
3answers
1k views
Nature of gravity: gravitons, curvature of space-time or both?
General relativity tells us that what we perceive as gravity is curvature of space-time.
On the other hand (as I understand it) gravity can be understood as a force between objects which are ...
7
votes
6answers
945 views
What determines which frames are inertial frames?
I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
8
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4answers
274 views
Would there be time dilation at the point where two gravitational fields cancel each other out?
My question is very simple, and most likely a stupid one:
One observer is at a point in space were the gravitational force form massive bodies (or a single massive body) cancel each-other out. The ...
7
votes
2answers
632 views
Do traversable wormholes exist as solutions to string theory?
There has been some heated debate as to whether the laws of physics allow for traversable wormholes. Some physicists claim we require exotic matter to construct wormholes, but then others counter the ...
6
votes
2answers
276 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
$$ T_{EH}^{\mu\nu} = -2 \frac{\delta ...
6
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3answers
702 views
Alcubierre Drive - Clarification on relativistic effects
On the Wikipedia article on the Alcubierre drive, it says:
Since the ship is not moving within this bubble, but carried along as the region itself moves, conventional relativistic effects such as ...
5
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1answer
254 views
In what limit does string theory reproduce general relativity?
In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) ...
4
votes
4answers
830 views
That 10km/day error predicted if GPS satellite clocks not corrected for relativity
Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite ...
4
votes
1answer
448 views
Lagrangian for Relativistic Dust derivation questions
In most GR textbooks, one derives the stress energy tensor for relativistic dust:
$$
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
4answers
418 views
What is a gauge transformation of the metric in GR?
I'm confused by this question:
Why can't General Relativity be written in terms of physical variables?
I can't quite see how you can make any change to the metric without either: (a) changing ...
1
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0answers
72 views
Showing that the Ricci scalar equals a product of commutators
I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
12
votes
3answers
702 views
No hair theorem for black holes and the baryon number
The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge.
For me it is puzzling why ...
11
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4answers
1k views
Is there a maximum possible acceleration?
I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity ...
8
votes
3answers
565 views
Special Relativistic approximation to GR
Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
7
votes
3answers
453 views
What is the exact gravitational force between two masses including relativistic effects?
I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 ...
7
votes
4answers
333 views
Why should one expect closed timelike curves to be impossible in quantum gravity?
From the Wikipedia article, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the Chronology ...
5
votes
2answers
396 views
Why is GR renormalizable to one loop?
I have read in a few places that GR is renormalizable at one loop. (hep-th/9809169 for example, second sentence, although they don't seem to develop this point at all). Is this do to some hidden ...
5
votes
2answers
620 views
Incompatibility Between Relativity and Quantum Mechanics
Why does Gravity distort space and time while the electromagnetic, strong, and weak forces do not?
Does this have to do with why Quantum Mechanics and Relativity are incompatible?
5
votes
4answers
546 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 ...
4
votes
3answers
138 views
How do you tell if a metric is curved?
I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - ...
4
votes
1answer
127 views
Is it possible for a black hole to form for an observer at spatial infinity?
To my knowledge if you calculate the coordinate time (time experienced by an observer at spatial infinity) it takes an infinite amount of time for an object to fall past the horizon of a Schwarzschild ...
4
votes
2answers
231 views
How much choice did Einstein have in choosing his GR equations?
General relativity was summarised by Wheeler as "Spacetime tells matter how to move; Matter tells spacetime how to curve". I have a fairly good mental picture of how the first part works.
However, I ...
4
votes
3answers
173 views
Twin paradox - observers counter orbiting Earth
Imagine three observers - one (A) stationary on the surface of Earth (latitude 0 deg) and two others orbiting the planet in the same circular equatorial orbit just in the opposite direction. When the ...
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 ...
4
votes
1answer
386 views
When will the Hubble volume coincide with the volume of the observable Universe?
The Hubble volume is the volume that corresponds to objects so far from the Earth that the space between us and them is expanding faster than the speed of light. (I.e. objects outside this volume ...
4
votes
8answers
608 views
Flat space limit of the Schwarzschild metric and Hawking temperature
The Schwarzschild metric reduces to the Minkowski metric in the limit of vanishing $M$, but the Hawking temperature which is proportional to $1/M$ diverges in the same limit. This would imply that ...
3
votes
2answers
497 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 ...
3
votes
1answer
372 views
What is a maximal analytic extension?
Can someone explain (as rigorously as possible) what is involved in analytically continuing, say, the Schwarzschild solution to the Kruskal manifold? I understand the two metrics separately but I'm ...
2
votes
4answers
313 views
Reducing General Relativity to Special Relativity in limiting case
I understand that general relativity is applicable to gravitational fields and special relativity is applicable to case when there is no gravity. But is there a derivation on how to reduce General ...
1
vote
1answer
229 views
Potential Energy in General Relativity
I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions:
In ...
23
votes
1answer
307 views
Overcharging a black hole
Hubeny's 1998 paper got a lot of people interested in determining whether cosmic censorship can be violated by dropping too much charge onto a black hole. It suggested that you might be able to get a ...
12
votes
3answers
310 views
Are gravitomagnetic monopoles hypothesized?
My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
7
votes
1answer
174 views
What is the generalization, if any, of the weak and dominant energy conditions to SUGRA?
In standard general relativity, we have the null energy condition, the weak energy condition related to stability, and the dominant energy condition related to forbidding superluminal causal ...
6
votes
3answers
281 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
votes
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?
5
votes
0answers
78 views
Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
5
votes
1answer
168 views
Is a black hole's surface area invariant for distant intertial observers?
Let's imagine I'm very far from any massive objects, so my local space-time is Minkowskian. Off in the distance is a black hole, far enough away that it doesn't noticeably curve space-time near me, ...
