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.

learn more… | top users | synonyms (1)

-1
votes
3answers
106 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 ...
63
votes
6answers
3k views

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 ...
0
votes
0answers
45 views

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
1
vote
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 ...
0
votes
0answers
35 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 ...
3
votes
2answers
87 views

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 ...
1
vote
3answers
123 views

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 ...
13
votes
3answers
800 views

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 ...
1
vote
0answers
64 views

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 ...
0
votes
3answers
55 views

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
votes
2answers
111 views

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 ...
0
votes
0answers
36 views

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 ...
1
vote
1answer
82 views

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 ...
1
vote
0answers
69 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 ...
1
vote
0answers
53 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?
1
vote
1answer
69 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 ...
0
votes
1answer
63 views

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 ...
3
votes
1answer
136 views

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 ...
0
votes
0answers
42 views

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, ...
0
votes
0answers
26 views

Derivation of Einstein-Infeld-Hoffman-Equation

According to Wikipedia, the general-relativistic three-body-problem can be solved using an equation derived by Einstein in 1938 ...
2
votes
1answer
50 views

Energy momentum tensor for a uniform spherical mass in general relativity

Can someone give the Energy momentum tensor for a uniform spherical mass in general relativity? I am particularly interested in the tensor expression outside the given mass. I am not looking for ...
1
vote
0answers
725 views

Apparently John Nash found a way to replace Einstein's theory of relativity days before crash [closed]

True story, John Nash told his friend that he revised Einstein's theory of relativity to account for quantum gravity days before dying in the car crash. This guy worked on manifold theory big time (in ...
0
votes
1answer
129 views

What happens when an object passes through the event horizon of a black hole in GR?

I've heard/read many times that in the general relativistic description of a black hole an object would pass through the event horizon unharmed (ignoring tidal forces) while quantum mechanics predicts ...
2
votes
2answers
55 views

What kind of volume does the event horizon of a Kerr black hole enclose?

I'm sorry if this is a naive question, I'm not too good with General Relativity. I'm aware that a rotating black hole is described by the Kerr Metric, and black holes of this kind have ring ...
1
vote
1answer
48 views

Is there a name for the linear quantity corresponding to the (quadratic) “interval $\Delta s^2$”?

Recently it has been affirmed here (again) that the quantity called "interval (also 'spacetime interval' or 'invariant interval')" is referring to two (in general distinct) events as arguments, such ...
1
vote
1answer
47 views

Bifurcate Killing Horizon of the Ads-Schwarzschild solution

I need your help. I'm considering the AdS-Schwarzschild solution: $ds^2=V(r)dt^2 + \frac{1}{V(r)}dr^2+r^2dΩ^2$ where $V(r)=1-\frac{2m}{r}+\frac{r^2}{l^2}$ with $m$ the mass of the black hole and $l$ ...
2
votes
0answers
116 views

Precession of Mercury (Python simulation)

I was trying to simulate the precession of Mercury based on the perturbed solution, and my questions about its implementation in python can be seen here: ...
0
votes
1answer
57 views

Cosmological Constant on the LHS of Einstein's Field Equation

The cosmological constant seems to be normally described as an energy (repulsive force, Dark Energy) of Space-Time. I was just wondering, if we were to interpret the cosmological constant as being ...
2
votes
1answer
149 views

Obtaining a copy of Hawking's Ph.D thesis - Properties of Expanding Universes

Due to its popularity, I am interested to know the 4 chapter titles and topics covered in S.W. Hawking Ph.D, Properties of Expanding Universes. I also ask this because that thesis is hardly available. ...
1
vote
2answers
57 views

First fundamental form in the Gibbons-Hawking-York boundary term

Let me expose my problem, I am trying to perform the explicit variation of the Gibbons-Hawking-York boundary term, $$S_{GH}=\int_{\partial M} d^{n-1}x\sqrt{\left|h\right|}K$$ The problem I have is ...
1
vote
2answers
274 views

Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
0
votes
0answers
39 views

Entropy of the boundary and stress-energy tensor in the bulk

The importance of this result cannot be understated: Positivity, monotonicity and convexity of relative entropy in the boundary is implied by the positivity of the stress-energy density tensor in the ...
0
votes
2answers
60 views

if singularities can be observed from the rest of spacetime, causality may break down

if singularities can be observed from the rest of space-time, causality may break down, and physics may lose its predictive power,i don't understand how it will happen?we don't have any idea what will ...
5
votes
5answers
312 views

Resolving General relativity and Newtonian mechanics to a computer [closed]

I know this is considered an old subject long ridiculed by many as the folly of layman. But I work in the field of computer simulation, specifically in producing fully functional 3D interactive ...
2
votes
2answers
88 views

If you fall in a black hole, when do you go past the event horizon? [duplicate]

Say I fall into the event horizon of a black hole. As I cross the black hole, I would appear to outside onlookers to freeze in time, and would never move from that point again. In my perspective, time ...
0
votes
0answers
29 views

Is there any matter inside an event horison? [duplicate]

Consider a feeding, growing black hole. We never observe any matter to cross the event horizon, because time stops there. All matter would be "stuck" in a sphere around the event horizon, slowly ...
2
votes
1answer
101 views

If the effects of gravity cannot travel faster than the “c”, does this mean we are only gravitationally bound by masses in our observable universe?

I'm 17 and fascinated by the differences and omissions Newton made in his equations of motion. However it makes sense that gravity can't travel faster than light because of the force-carrying ...
0
votes
1answer
50 views

Using metric tensor to contract

Can the metric tensor also contract the indices in the $$\epsilon^{\tau\lambda\mu\nu}~?$$ For example, if we have ...
0
votes
1answer
42 views

Influence of spacetime curvature on electromagnetic wave propagation [duplicate]

Classical physics assumes that spacetime is evenly distributed in the sense that Coulomb's Law predicts that a charged particle will create a spherically symmetric electric field around its location. ...
2
votes
2answers
124 views

Do clocks measure conformal time (new argument)?

Assuming the spatially flat FRW metric for simplicity: $$ds^2=c^2dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ where $t$ is cosmological time, $a(t)$ is the scaling factor and $x,y,z$ are co-moving spatial Cartesian ...
3
votes
3answers
150 views

Is an event horizon absolute to all observers?

Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon (disregarding effects of tidal ...
0
votes
1answer
37 views

The significance of the pressure term within the momentum-energy tensor [duplicate]

EDIT: this question is based around my notion regarding the possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$, The answer below resolves the question and I have deleted ...
0
votes
1answer
75 views

Suggestions for GR solved problems books

Study Topic: General Relativity I'm looking for a recommendation for either a dedicated problems and solved solutions book or, failing that, a textbook with a separate comprehensive solutions ...
0
votes
0answers
48 views

Contraction of Kronecker delta = 4 [duplicate]

This suggests, as a shortcut notation, the concept of lowering indices; from any vector we can construct a (0, 1) tensor defined by contraction with the metric: $$A_\nu ≡ g_{\mu\nu}A^\mu$$ so that ...
1
vote
1answer
73 views

Confusion about two forms of connection coefficients

I am new to GR. In one book I found that the connection coefficient expression is given by $$ \Gamma^\mu_{\nu\lambda} = -\frac{1}{2} g^{\mu\rho} (\partial_\nu g_{\lambda\rho} + \partial_\lambda ...
0
votes
2answers
77 views

“Shortest” path in general relativity

My professor in mechanics course sneakily teach us some basic idea of general relativity. Which one of the basic assumption is particle walks in shortest world line. I understand shortest path in ...
1
vote
1answer
60 views

How much is time slowed down inside a planet or star?

An answer to What would be the rate of acceleration from gravity in a hollow sphere? states "that according to General Relativity time passes more slowly inside a hollow massive sphere than it does ...
0
votes
0answers
27 views

1. How is Newtonian calculations compatible with curved spacetime? and 2. multiple competing reference frames for gravity [duplicate]

Since spacetime is curved, and since the measurement of distance on a curve is along a geodesic, how is it that Newtonian (non-curved) physics can be successfully deployed to calculate distances, ...
0
votes
0answers
28 views

Vector fields corresponding to null geodesic congruences in general relativity

I'm working in Minkowski space, and I'm considering some 2D surface, $S$. On each point of the surface, I've computed a null vector, $k^a$, which is orthogonal to it. There will be a unique null ...
2
votes
1answer
102 views

Can Bosons couple to gravity? Why do we need vielbein?

It is said that In theories such as Supergravity where there are fermions coupled to gravity, one must use an auxiliary quantity, the frame field (vielbein). In supergravity, can a boson be coupled ...