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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34 views

Looking out from a collapsing star

From the perspective of the surface of a collapsing star, if you were riding it in as it formed a black hole, what would you observe looking out into the rest of the universe? As you approached the ...
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1answer
65 views

How do I derive geodesic equation using variational principle? [duplicate]

I am trying to derive the geodesic equation using variational principle. My Lagrangian is $$ L = \sqrt{g_{jk}(x(t)) \frac{dx^j}{dt} \frac{dx^k}{dt}}$$ Using the Euler-Lagrange equation, I have got ...
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1answer
73 views

Integrating the geodesic equation to obtain Newtonian energy of test particle

I am studying General Relativity, and have come across a question that I am finding rather intractable: In Newtonian Theory, the energy equation for a test particle in orbit around a point mass ...
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2answers
1k views

Evidence for quantum gravity from gravitational waves

The rumor spreads that physicists will make their big gravitational wave announcement this thursday. I am far from being an experimentalist, but I want to know if there is any chance that the ...
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0answers
47 views

Are objects like $a^{\mu \nu} a_{\mu \nu} b^{\mu \nu}$ consistent with Einstein summation?

I'm familiar with Einstein' summation notation and I understand objects like $a^{\mu \nu} a_{\mu \nu}$ just fine. But I'm wondering why I've never come across objects like this: $a^{\mu \nu} a_{\mu \...
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33 views

Identity $ \epsilon_{abcd} R^{cd}_{\phantom{cd}mn} = \epsilon_{mncd} R^{cd}_{\phantom{cd}ab}$ in vacuum

starting from \begin{align} \epsilon_{\rho\lambda\xi \kappa} R^{\xi \kappa}_{\phantom{ab} \sigma\tau} + \epsilon_{\rho\sigma \xi \kappa} R^{\xi \kappa}_{\phantom{ab} \tau \lambda} + \epsilon_{\rho \...
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3answers
83 views

Twins paradox question [duplicate]

In the twins paradox, the twin that travels away from earth comes back to find that his (her) twin has aged much more due to relativity's effect on time. Why can't we posit that it is not the one twin ...
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0answers
52 views

What is conformal symmetry physically?

I'm reading a paper by t'Hooft http://arxiv.org/abs/1410.6675. There is an argument in the paper that I could not understand: "Now that system, described by Maxwell’s equations, does have conformal ...
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1answer
49 views

In the orthonormal tetrad method, what is the relation between basis one forms and commutation coefficients?

If $\omega_i$ are dual basis one forms corresponding to an orthonormal tetrad basis $e_i$, and given that the commutation coefficients $C_{ij}^k$ are defined by \begin{equation} [e_i,e_j]=C_{ij}^k ...
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2answers
437 views

How does one actually use the Einstein field equations?

I'm experimenting with the Einstein field equations (EFE) and I'm wondering how to actually use them. It seems to me that the simplest are those evolving a vacuum, which imply that the stress-energy-...
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1answer
114 views

How can space and time occur spontaneously? [closed]

In the book: "A universe from nothing" by the theoretical physicist Lawrence Krauss he mentions that space and time can occur spontaneously. Unfortunately he does not explain how. So my question is, ...
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1answer
101 views

Quantum teleportation + time dilation = time travel? [closed]

Thought of this a while back and thought it was pretty funny, not sure if there's been similar ideas discussed elsewhere. I can think of at least 2 reasons this won't work: 1) As far as I know, "...
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1answer
117 views

Non-Euclidean mechanics; is it useful?

Special relativity has the following single-particle Lagrangian: $$S = \int_{t_0}^{t_f}\sqrt {\langle \mathrm d\vec{s},\mathrm d\vec{s}\rangle}.$$ Clearly it is based on Euclidean norms; it is in ...
2
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0answers
50 views

Where other frame observer will put new stick [closed]

my question is with relativity, if we draw two circle of same radii and fill the perimeter with stick (very small so it cover whole perimeter) now if we rotate a stick with veey high speed ...
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0answers
45 views

A problem with ADM mass in the derivation of 1st law of black hole thermodynamics

The definition of ADM mass is $$M=\frac{1}{16\pi}\lim_{r\rightarrow\infty}\int \left(\frac{\partial h_{\mu\nu}}{\partial x^\mu}-\frac{\partial h_{\mu\mu}}{\partial x^\nu} \right)N^\nu dA$$ according ...
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0answers
90 views

Gravitational waves: novel or confirmatory? [duplicate]

If the rumors are true and gravitational waves have been detected, would we learn any new fundamental physics from them? Or is this simply an important confirmation of a prediction of general ...
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1answer
47 views

Gravity, Acceleration, Time Dilation and the Equivalence Principle

Three clocks are started at exactly the same time on Earth. The first and second clocks are taken into the vacuum of space. The first clock accelerates until it reaches 100,000m/s, then stays at this ...
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1answer
85 views

Components of dual vectors

(This is a close retelling of Wald, problem 2.4b. Not for homework; just curiosity and an increasingly alarming suspicion that I've never actually understood anything.) Let $Y_1 ... Y_n$ be a ...
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2answers
63 views

Is there a doppler effect on the images of stars around rotating black holes?

I'm an illustrator working on a project involving rotating black holes like those discussed in "Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar" by James, ...
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1answer
72 views

Divergence of inverse of metric tensor

I know that the Levi-civita connection preserves the metric tensor. Is the divergence of the inverse of metric tensor zero, too?! I'm not so familiar with the divergence of the second ranked tensor. ...
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1answer
102 views

Evaporating black hole Penrose diagram

The context for this is the diagram from From where (in space-time) does Hawking radiation originate? - the more I think of it, the less it makes any sense ) This particular question is about ...
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1answer
70 views

When is a spacetime a black hole?

While reading $\textrm{Present status of the Penrose Inequality}$ by Marc Mars, 2009, I was confused with the following statement: ... in order to determine whether a space-time is a black hole, ...
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2answers
144 views

Does time have a minimum 'speed'?

Sorry if this is an ignorant question, but I've been having some trouble grasping some concepts related to time dilation. So far, my understanding of the concept says that if I am in a certain frame ...
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0answers
51 views

Worldlines in Schwarzschild geometry

I have an observer and a photon on a hypersurface $ \theta=\pi/2$ . My observer has $e, l$ constants of motion (energy and angular momentum divided by mass) and photon has $e',l'$. What conditions ...
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4answers
298 views

Up or Down? A Question about Relativity

The standard text discussion of the equivalence principle and the bending of light rays goes like this. We, as observers watch a glass elevator ascending. A light beam is fired from left to right. The ...
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1answer
70 views

Graviton detector thought experiment

I was recently thinking of a thought experiment: Assumptions Graviton detectors can exist The equivalence principle will hold in the final theory of quantum gravity We can accelerate the graviton ...
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1answer
105 views

Big Bang Quarks Travelling at Light Speed [closed]

When I think of an explosion it lasts a fraction of second. When the entire mass of the universe explodes how much time passes before the perfect sphere slows from traveling at/near the speed of light ...
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1answer
110 views

What does it look like for a ball falling to the event horizon observed by distant static observer?

Here is the picture used in susskind&Lindesay's book ''An Introduction to Black Holes, Information and String Theory Revolution'' I understand very well that the ball will be contracted at the ...
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1answer
48 views

Conditions at black hole's event horizon

This question had, at least partially, been discussed here before, but I feel that the record has not been set straight. There seem to be lack of agreement regarding conditions (like gravitational ...
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0answers
46 views

Two black holes prepared from different initial states

I have asked a similar question, I would like to reformulate it in more details. Here is a thought experiment: Assuming we can create black holes by squeezing photons, we can then prepare two ...
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0answers
21 views

Mass dilation in general relativity [duplicate]

Does mass dilate in general relativity. For example if I was accelerating will my mass dilate? Thanks
1
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1answer
69 views

Kaluza Klein Equations of Motion

I have found a derivation of the Kaluza-Klein equations of motion on this webpage: http://www.konfluence.org/Williams_31Mar2012.pdf As I understand it, he starts with the 5d geodesic equation of ...
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3answers
565 views

Age of the universe versus absolute time [duplicate]

In Wikipedia, the age of the universe is defined as the "time elapsed since the Big Bang" while "time" links to "the cosmological time parameter of comoving coordinates" which itself links to "the ...
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2answers
114 views

Shouldn't General Relativity Predict a Maximum Temperature?

I've seen a lot of questions about maximum temperature and “absolute hot” — several ask if special relativity places any limits on temperature (clearly not). (Also this discussion of absolute hot on a ...
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0answers
17 views

Do have Geodesic equation of motions (GR) have any practical use in control theory to control e.g. a rocket on Lunar/Mars space flights? [closed]

I just wonder, if Geodesic equation of motions derived from the GR field equations have any practical application in control theory? So far all books I came across always use Newtonian Forces to ...
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0answers
40 views

Is it possible that Gravity is a Repulsion phenomenon instead of an attractive “force”? [duplicate]

The classical saying is to say that gravity is an "Attractive" force meaning that massive objects like a planet will attract other massive objects like an apple. But is it not actually the empty space ...
1
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1answer
83 views

Mass and time relativity [duplicate]

In the space between galaxies in the absence of matter, would time run faster than inside a galaxy? A black hole can slow time. Is there a cosmic opposite of that effect on time? Like the following ...
2
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1answer
85 views

Surface gravity of a Killing horizon

I have two questions about this: 1, Surface gravity is defined on the Killing horizon by $\xi^\mu \nabla_\nu \xi^\nu = \kappa \xi^\nu$ for the Killing vector $\xi$. Why can we interpret this as the ...
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1answer
205 views

When will Einstein's theories become laws? [closed]

Einstein theories , specifically relativity, have been fascinating us for around 100 years yet with all the real and actual evidence of its validity we still consider it a "theory"..... How much more ...
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1answer
49 views

Angle of deflection in gravitational lensing

We are currently studying general relativity in school and also had a brief look at gravitational lensing. My teacher gave us the angle of deflection between the apparent location of a star and its ...
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0answers
32 views

Travelling backwards in time - is it possible? [duplicate]

Einstein predicted that gravity bends spacetime such that travelling through time is possible; but only forward in time. According to General Relativity we can travel in the future, but not backwards ...
2
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0answers
77 views

Are all spacetimes locally conformally flat?

No, is the answer. However, I am confused. Let $M$ be a (2+1) Lorentzian manifold (for simplicity) . Then the line element is given by : $ds^{2}=g_{\mu\nu}dx^\mu dx^\nu=−N^2 dt^2 + γ^{ij} (dx^i + ...
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0answers
23 views

Radiation collapse to black hole

I want to find the temperature at which radiation in AdS will collapse to form a black hole. I have even found a reference that gives the answer but I cannot understand it: http://srv2.fis.puc.cl/~...
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47 views

If black hole is equivalent to a planet of same mass for a distant observer, then why does 'excess radius formula' require uniform mass density?

I understand that the spacetime curvature of a non-rotating, uncharged black hole is identical to that of a planet with same mass/energy for an observer at a distance farther than the radius of the ...
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0answers
49 views

How come the cosmological constant supports the idea of dark energy existing? [duplicate]

According to an article I've read recently, the cosmological constant was used to support the theory of dark energy. But the cosmological constant already defines an inclination in the essence of ...
2
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0answers
64 views

What is really going on in the ergosphere of a Kerr black hole?

Considering the Kerr metric with $GM>a$, we can compute 2 event horizons: $r_\pm=GM\pm \sqrt{G^2M^2-a^2}$ These event horizons are null surfaces, and trajectories are timelike between $r_+$ and $...
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1answer
118 views

Black Hole Heat Capacity

Why is the specific heat capacity of a black hole given by $C=\frac{\partial M}{\partial T}$? Heat capacity should be ratio of heat change to temperature change so, denoting heat by $Q$, we have $C=\...
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1answer
66 views

Tensor indices and row and column labels of corresponding representation matrices

When reading undergraduate GR literature, I often see that the authors represent tensors ${\eta^\alpha}_{\beta}$, ${\eta^\beta}_{\alpha}$, $\eta_{\alpha \beta}$, $\eta^{\alpha \beta}$ as matrices. ...
2
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1answer
63 views

Is $E = p^0$ in non-inertial frames?

In special relativity the energy of a particle is the 0-component of the 4-momentum. However, is this still true in non-inertial frames, and in particular in non-freely-falling frames in general ...
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54 views

Is metric $g$ a representation of Lorentz group? What decides it's transformation properties?

I am confused what representation of Lorentz group does a metric transform under? How does it's transformation properties are decided?