A theory that describes how matter interacts dynamically with 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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Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
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Proof that Energy Momentum Tensor of Scalar Field Theory satisfies Weak Energy Condition

It's a question on Sean Carroll's Spacetime and Geometry, where we are supposed to prove that the energy momentum tensor of scalar field theory satisfies Weak Energy Condition (WEC). The energy ...
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755 views

Why is spacetime near a quantum black hole approximately AdS?

In this link, one of the answers contains the statement If you examine the space-time near a finite area quantum black hole, you will see an approximate AdS space. Presumably "approximate" ...
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Why dynamic Casimir effect does not appear in static gravity field?

Dynamic Casimir effect tells us that a constantly-accelerated mirror should emit radiation due to interaction with vacuum. Following principle of equivalence, a similar mirror placed in static ...
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432 views

How can I vizualize and understand curved spaces in general relativity?

I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle ...
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170 views

General parameters of the stress energy tensor in local inertial frame

A general 4x4 symmetric tensor has 10 independent components. How many components are we free to prescribe in the local inertial frame? For example, relativistic dust is $\mbox{diag}(\rho c^2, 0, 0, ...
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554 views

Lagrangian for Euler Equations in general relativity

The stress energy tensor for relativistic dust $$ T_{\mu\nu} = \rho v_\mu v_\nu $$ follows from the action $$ S_M = -\int \rho c \sqrt{v_\mu v^\mu} \sqrt{ -g } d^4 x = -\int c \sqrt{p_\mu ...
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What is wrong in this representation of relative reference systems?

Up until now I've explained relative time to myself as looking at the 3D world from different four-dimensional perspectives, analogous to how looking at a 2D-ish object (eg. a sheet of paper) from ...
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4answers
646 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 ...
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If photons are deflected by a strong gravitational field, then how come photons do not have mass? [duplicate]

Possible Duplicate: Explain how (or if) a box full of photons would weigh more due to massless photons It has been proved and showed through experiments that light can be bent by the Sun or ...
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735 views

Need some basic help with notation and the Christoffel symbols

Apologies in advance if some of the questions below seem overly simple. In an introductory GR book, I find the following expression for the autoparallel of the affine connection (the upper bound of ...
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334 views

how many times have the first photons lapped the universe?

I'm not really interested in the actual number of times, but rather an explanation of a closed Universe. How do we still measure the background radiation of the Big Bang? Those electromagnetic waves ...
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6answers
561 views

General Relativity research and QFT in curved spacetime

A naive question: Are these subjects, i.e. classical GR and QFT in curved spacetime, being worked upon much anymore? Who is researching this and what are the problems within these fields? Any ...
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1answer
605 views

How do we know the geodesic is a minimum?

The geodesic equation is derived from the Euler-Lagrange equation, which (as I understand it) is a necessary but not sufficient condition to ensure that the geodesic is a minimum. The introductory GR ...
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311 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?
3
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2answers
251 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 ...
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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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160 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
230 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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686 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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3answers
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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
301 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
290 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
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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
335 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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419 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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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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230 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
996 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
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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
205 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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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 ...
7
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70 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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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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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
172 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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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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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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442 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
148 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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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
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2answers
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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
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1answer
231 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
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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 ...
5
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3answers
324 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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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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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
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133 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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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
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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, ...