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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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 ...
7
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1answer
246 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 ...
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2answers
157 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 ...
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1answer
207 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 ...
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1answer
544 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 ...
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2answers
2k views

Value of the Hubble parameter over time

There is something I don't understand about the Hubble parameter $H$, 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 ...
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0answers
258 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
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1answer
267 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 ...
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2answers
188 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 ...
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2answers
294 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 ...
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2answers
406 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 ...
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4answers
3k 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 ...
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2answers
215 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 ...
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1answer
878 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 ...
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3answers
1k 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 ...
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1answer
185 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 ...
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2answers
3k views

What is the physical meaning of 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
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2answers
67 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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4answers
382 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 ...
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4answers
695 views

The Sun as a gravitational lens

Since the Sun is a gravitational lens with as focal length of 550 AU for visible light, with an immense amplification factor, shouldn't it light up objects hanging out there? We should get solar ...
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1answer
157 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 ...
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3answers
865 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 ...
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3answers
193 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 ...
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2answers
412 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 ...
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1answer
141 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 ...
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297 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 ...
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2answers
389 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 ...
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1answer
224 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 ...
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4answers
1k 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 ...
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3answers
306 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 ...
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2answers
1k 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 ...
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93 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.
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0answers
122 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 ...
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2answers
646 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 ...
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1answer
193 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, ...
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2answers
878 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?
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0answers
116 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 ...
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3answers
5k 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 ...
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1answer
168 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 ...
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1answer
221 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 ...
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4answers
603 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 ...
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3answers
576 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 ...
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2answers
171 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
434 views

Could a ship equipped with Alcubierre drive theoretically escape from a black hole?

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?
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2answers
724 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 ...
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2answers
323 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 ...
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1answer
273 views

What is a black hole?

Is there a definition of a black hole in a generic spacetime? In some books, for example Wald's, black holes are defined for asymptotically flat spacetime with strong asymptotic predictability, ...
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410 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 ...
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1answer
480 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 ...
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457 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 ...