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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Gravitational potential in GR

In proving that the metric will play the role of gravitational potential, there is this chain of ideas: ...
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48 views

Will the rotation of a neutron star prevent it becoming a Black Hole?

This question, to me anyways, is basically a balancing act between 2 possibly opposing effects. Take a neutron star with just too small a mass to overcome it's degeneracy pressure, failing to ...
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42 views

Does the total particle energy increase in FRW Universe?

If a particle travels on a geodesic with 4-momentum $P^\mu$ in a spacetime with a Killing vector $K_\mu$ then we have a constant of motion, $K$, given by: $$K=K_\mu P^\mu$$ Using the relationships: ...
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Do Einstein's equations allow multiple solutions that agree in a neighborhood of a spacelike hypersurface?

This question is an extension of my a question that I have recently asked: Why doesn't a global frame of reference exist for GR?, where it was recommended that I post another question (so I am ...
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22 views

Expansion of universe faster then speed of light? [duplicate]

Watching one of the shows on discovery channel, I got to know that during the starting phase of universe its speed should have been faster then speed of light. But then didnt einstein say that nothing ...
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5answers
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Why do we need coordinate-free descriptions?

I was reading a book on differential geometry in which it said that a problem early physicists such as Einstein faced was coordinates and they realized that physics does not obey man's coordinate ...
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41 views

Interpretation for negative energy of curves

Let $(M,g)$ be a Lorentz manifold and $\gamma :[a,b] \to M$ a differentiable curve. I understand we define the energy of $\gamma $ as: $$E[\gamma] = \frac{1}{2} \int_a^b ...
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1answer
71 views

Are moving objects producing stronger gravity fields? [duplicate]

If the strength of gravitational influence exerted by a body is derived from its mass and energy then is it true that a moving object which has some kinetic energy should also produce stronger ...
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79 views

Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
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81 views

What experience tells us that gravitational acceleration cannot vanish everywhere?

In attempt to describe the consequences of the Equivalence Principle, Papapetrou in his book, said: When there are gravitational accelerations present, as for example in the gravitational field of ...
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63 views

Explosion in a sphere and the Gravitational field outside

Take a hollow sphere and conduct a process on the inside, which transfers mass into kinetic energy (e.g. we let a big nuclear bomb detonate or something like that). For simplicity, assume that this ...
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107 views

What is a Null Geodesic? [duplicate]

What is a Null Geodesic? My textbook only explains it as the Minkowski metric which equals to zero, but I'd appreciate a more detailed explanation.
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68 views

Invariance in general relativity, university in problems question

From Problem #5 here, Free falling particles' worldlines in General Relativity are geodesics of the spacetime, i.e the curves $x^\mu(\lambda)$ with tangent vector $u^\mu=dx^\mu/d\lambda$, such ...
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17 views

Why can't our universe be spherical? [duplicate]

if we happen to follow the bigbang singularity hypothesis, when he explosion occured shouldn't it expand in all directions. Seemingly our universe shouldn't have any boundaries. I searched for the ...
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0answers
54 views

Is the Big Bang notion compatible with the flat space? (A problem with the **moment** of Big Bang, not with the place of it) [duplicate]

A passage from a paper: "If one imagines running the clock backward in time, any given region of the universe shrinks and all galaxies in it get closer and closer until they smash together in ...
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2answers
141 views

Why doesn't a global frame of reference exist for GR?

I only have at best a layperson's familiarity with GR, so forgive me if I am asking a basic question, but I have heard that in GR, we cannot have a global frame of reference, that is a frame of ...
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Different signatures

I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I ...
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Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
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60 views

Stationary v/s Static

Blau, in his GR book, says that a stationary and spherically symmetric metric is automatically static. He says this easily follows from the fact that for a stationary metric, and in spherical ...
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Hawking Temperature of the BTZ Black Hole

The metric of the BTZ Black Hole is given by $$ ds^2 = - N^2 dt^2 + N^{-2} dr^2 +r^2(d\phi + N^\phi dt)^2 $$ with $$ N^2 = -M+ \frac{r^2}{l^2} + \frac{J^2}{4 r^2}, \ \ \ \ \ \ N^\phi = ...
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Spherical Symmetric Metrics

In the case where all books try to illustrate a spherical metric, the procedure goes this way: First they impose isotropy in terms of polar coordinates so that one can write: $$ds^2=-A(r)dt^2 + ...
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Calculating time dilation

I'm writing a science fiction story where the protagonist's experience requires long intervals between events. My plan is to put him/her/it on a spaceship between events at an appreciable percentage ...
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1answer
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Is a planets orbit really a straight line through curved spacetime? [duplicate]

My understanding is that general relativity concludes that gravity isn't real because it does not exist in all frames of reference. Also that mass and energy warp spacetime into a curved geometry. ...
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80 views

How to show flat FRW metric has a time-like conformal Killing vector?

I would like to derive the fact that the flat FRW metric has a time-like conformal Killing vector. Is there an easy way to do this? @ValterMoretti showed how one can do this for metrics with a ...
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4answers
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Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?

I am generally interested in the role of "pings"(0a) between participants (a.k.a. "signal roundtrips"(0b), as familiar for instance from Synge's "five point curvature detector") in the determination ...
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Is there a natural (suitable) definition for functional derivative in Curved space time

If $$\delta S = \int \sqrt g F[\phi] \delta \phi\tag{1}$$ Then is it natural to define the functional derivative as follows, $$\frac{\delta S}{\delta \phi} = F[\phi].\tag{2}$$ In particular does ...
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Can gravitational waves carry momentum, and if so what mass/energy produces it, and is space-time capable of vortex formation?

This question is about gravitational waves postulated by Einstein. Is gravitational radiation a form of mass/energy that can form momentum? If it causes ripples in space-time, would space-time ...
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Weinberg-Witten theorem and Landau pseudotensor, or how QFT can make prediction about GR

Weinberg-Witten theorem states that there isn't Poincare covariant stress-energy tensor for massless fields with helicity more than $1$. The only example of such higher helicity field is graviton. ...
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Conformal time-like Killing vector near null geodesics in all spacetimes?

Is it true that in all spacetimes there is some conformal time-like Killing vector $\tau^a$ in the vicinity of null geodesics? If the above statement is true then can one argue that, for all ...
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2answers
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How are FRW metric and Minkowski metric physically different?

According to GR, matrices are coordinate invariant. Does this mean we can transform FRW metric to Minkowski metric with a coordinate transformation like $$dx'=dx\cdot a(t), dy' = dy\cdot a(t), dz' = ...
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1answer
64 views

Time dilation and space time [closed]

I know a little about space time, and I know that space time is adding the time component into the three- dimensional world and creating an abstract universe. But my question is that why time is ...
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3answers
109 views

Does it make sense to model the Universe from an outside perspective? [closed]

I was reading some questions and answers about black holes and whether matter can actually pass through the apparent horizon, in particular this one: How can anything ever fall into a black hole as ...
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6answers
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Thought experiment - would you notice if you fell into a black hole?

I've heard many scientists, when giving interviews and the like, state that if one were falling into a black hole massive enough that the tidal forces at the event horizon weren't too extreme, that ...
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Is there any explanation for these objects apparently traveling faster than light? [duplicate]

This is from a documentary on the science channel: https://www.youtube.com/watch?v=RaELad94KZs
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1answer
61 views

Does GR put a theoretical lower limit on the radius of a black hole event horizon?

Within GR theory, without going to the extreme r/0 as a radius, (but approaching that as an asymptotic case), is there any theoretical limit as to how small the event horizon of a rotating and/or ...
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37 views

Symmetry of the Gravitational Stress Energy pseudo tensor

Recently, I have been reading on the Gravitational Stress-Energy pseudo tensor. It says in Wikipedia that one of the conditions for a suitable GSE pseudo tensor is that it has to be symmetric about ...
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Can I simply reverse the indices in a contraction?

Suppose I have something like $$ \left( \nabla_\mu \nabla_\beta - \nabla_\beta \nabla_\mu \right) V^\mu = R_{\nu \beta} V^\nu $$ Can since all the terms involving $\mu$ on the left and $\nu$ on the ...
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3answers
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Is simultaneity in SR only a pedagogical tool?

In a very recent post here I recently learned that simultaneity has no meaning in general relativity; I can accept the answer and explanation that was given for that question. But then Harry Johnston ...
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Is simultaneity well defined in general relativity?

In special relativity for each event and reference frame we can find a plane of simultaneous events. I wonder is it possible to do the same in general case in curved space? Is simultaneity even ...
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Does gravitational pull depend on the velocity of movement?

In classical mechanics the gravitational pull doesn't depend on the velocity. It's the same regardless if the body stands still or moves. In general relativity, the test particles follow geodesics ...
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Energies of bodies travelling on different geodesics

If two bodies of equal mass are released at rest from point $A$ and travel on different geodesics in a curved spacetime to point $B$ will they have the same total energy at point $B$? Is the same ...
5
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2answers
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By what process did the era of inflation end, or has it just slowed down (a lot)?

Could someone please explain the current model regarding: a) how the era of inflation was turned off (the graceful exit idea or alternatives)? b) what the timeline is between the era of inflation ...
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Test bodies general relativity

I'm studying section 82 of the Landau & Lifshitz Field Theory vol.2 In this page it's written that the relative position of test bodies can't remain unchanged during time. And ok with this. But ...
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1answer
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Covariant derivative ordering

I was working on a problem involving Bianchi identities, in a particular case I have to take the covariant derivative of the following, which indeed is the Ricci tensor in linearised limit ...
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76 views

Does negative mass reverse the arrow of time?

General relativity predicts that normal mass (positive mass) results in the curvature of spacetime which in return leads to gravitation. Since space and time are bonded together, any change on the ...
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56 views

Why are the integral form of the GR equations problematic?

I have heard that working with the integral form of the GR equations is problematic - relative to determining a Greens function. Can someone explain the details as why?
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70 views

Static De Sitter Metric

For static dS metric we have $$x_{0}=\sqrt{H^{-2}-r^{2}}\sinh(Ht)$$$$x_{1}=\sqrt{H^{-2}-r^{2}}\cosh(Ht)$$ and the metric can be written as $$ds^{2}=-dx_{0}^{2}+dx^{2}_{1}+d\bar x$$ where the barred ...
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How are these two Riemann tensor equations equivalent?

Poisson in A Relativist's Toolkit defines the Riemann tensor as$$A_{\,;\alpha\beta}^{\mu}-A_{\,;\beta\alpha}^{\mu}=-R_{\phantom{\mu}\nu\alpha\beta}^{\mu}A^{\nu}.$$ Foster and Nightingale's A Short ...
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How can I make two separate equations for Christoffel symbols give the same answer?

I have been studying the covariant derivative and I'm confused by the calculation of the Christoffel symbols $\Gamma$. The equation for computing $\Gamma$ is given as: $${\Gamma^c}_{ab} = \frac12 ...
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Flat Slicing De Sitter to Static De Sitter

I wonder how one transforms from flat slicing de sitter metric given below $$ds^2=-dt^2+e^{Ht}d\bar r^2$$ where $H$ is Hubble expansion rate as a function of time, to static coordinate, ...