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
vote
1answer
151 views

Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
3
votes
3answers
195 views

How does warped space actually look (visually)?

Recently, I was reading about space warping due to extreme gravity and at speeds approaching c, but in books, they always show space in 2D and depth to show space distortion. I was wondering how ...
0
votes
1answer
53 views

Can't derive FRW Christoffel symbol [closed]

I'm trying to confirm that the $\Gamma^1_{01}$ Christoffel symbol of the FRW metric is $\dot{a}/a$. I have the FRW metric: $$ds^2=-dt^2+a(t)^2\left[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+\sin^2\theta\ ...
0
votes
0answers
29 views

Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
1
vote
1answer
62 views

Uncertainty principle within a neutron star or black hole

Take the time-energy uncertainty relation, $\Delta$$E$$\Delta$$T$$\ge$$\hbar/2$. My question is based on my confusion about the effect this relation may have within the interior of a highly ...
4
votes
1answer
61 views

Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
0
votes
0answers
15 views

A Relativity question about radial acceleration? [duplicate]

How do you calculate the radial acceleration of a stationary observer in the Schwarzschild coordinates? I have calculated the 4-velocity and 4-acceleration but not sure how to proceed?
2
votes
2answers
168 views

Relativity question about 4-velocity

Given a 4-velocity $u^0$, how do you find $u_0$? Do you use $u_{\alpha}u^{\alpha} = -1$?
2
votes
1answer
37 views

When does light reach a shell observer in Schwarzschild metric?

I am trying to simulate the trajectory of light in the Schwarzschild metric (as seen by a far away observer) with fixed $\theta = \pi/2$. According to my source (Chapter 18, section 18.5) the ...
1
vote
0answers
29 views

Tangent Vector Field from Metric

Question: Starting from an arbitrary spacetime metric, how does one obtain a tangent vector field? (We might need to assume certain geodesic congruences but my understanding is very limited.) Build ...
2
votes
0answers
40 views

Question about wormholes with ends moving relative to one another [duplicate]

Let's say the two ends A and B of a wormhole are moving relative to one another. If I stick a starship halfway into end A of the wormhole, does the part of the starship that sticks out of end B move ...
3
votes
1answer
43 views

Do we weigh more when standing near massive buildings?

I'm very new to the concepts of SR/GR and curvature of spacetime. My understanding is that the bending of spacetime is the causation of gravity, and that matter is the causation of the bending of ...
0
votes
1answer
62 views

A general relativity question about the Einstein equations?

Assuming a Robertson-Walker metric to describe homogeneous and isotropic cosmological models, Einstein equations with cosmological constant reduce to these 3 non-linear ordinary differential equations ...
11
votes
4answers
2k views

Does General Relativity imply loops in space?

Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In ...
1
vote
2answers
91 views

Is the time “direction” in General Relativity equivalent to a spatial volume [closed]

Most G.R.textbooks introduce time as an extra dimension, i.e. -ict. (see EDIT below for clarification). So although I can not mentally imagine this, I think of it as an extra line, "orthogonal" to the ...
0
votes
0answers
25 views

DGP brane world model

Can we think of interaction between dark energy and dark matter within the brane in DGP model like in case of GR?
2
votes
1answer
89 views

What are Einstein constraint equations?

Yesterday, I met Einstein constraint equations in a thesis? I failed to understand them. Do they have physical meaning? And what do they "constrain"?
1
vote
0answers
50 views

Momentum conservation in FRW spacetime

The spatially flat FRW metric in Cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it, since the metric does not depend on the spatial co-moving ...
1
vote
1answer
47 views

Seeing in shell reference frame in general relativity

I'm trying to understand how an observer in a shell reference frame sees an object (star) near a black hole. I'm specifically trying to understand the equation: $$\tan \theta_{shell} = ...
2
votes
2answers
71 views

Schwarzschild metric: motivations and applications in physics

I have a mathematical background and I have just derived the expression of the Schwarzschild metric. Now I was wondering what were the motivations and applications in physics of this metric. Any info ...
2
votes
0answers
119 views

$AdS_2$ Black Hole [closed]

I know that $AdS_2$ black hole has the following metric: $$ ds^2=(r^2-a^2)dt^2+\frac{dr^2}{r^2-a^2}.\tag{1} $$ Here $a$ is constant. On the other hand I am regularly facing with the following ...
1
vote
0answers
34 views

Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
0
votes
1answer
73 views

Laplace-Beltrami vs d'Alembert operators in flat vs curved space-time

I am confused with the difference between Laplace-Beltrami (LB) and d'Alembert operators in flat/curved space-time. d'Alembert operator in flat space-time (Minkowski) is defined as $$\Box= ...
1
vote
3answers
72 views

Relativistic rigid motion

In Bryce DeWitt's Lectures on Gravitation, in eq. 2.7 on page 25 when he describes the rigid motion of a continuum he states $$x^\mu(\xi,\tau)=x^\mu(0,\sigma)+\xi^in^\mu_i(\sigma)\,\,\,(i=1,2,3) \, ...
0
votes
1answer
40 views

Observers in different planets viewing each other

I'm a newbie to relativity, so If the question is idiotic, please excuse me. My question is, as in Interstellar movie suppose one person is sitting in a planet A whose 1 hour equals to 6 years of ...
0
votes
1answer
65 views

Fibre bundles and space-time

I'm having some trouble understanding the concept for this more than likely due to my lacking mathematical background. I am currently reading Roger Penrose's The Road to Reality page 394 ...
6
votes
2answers
128 views

Intuitive understanding of the elements in the stress-energy tensor

There is an image in the Wikipedia about the stress-energy tensor: I have a rough understanding of the stress tensor: you imagine cutting out a tiny cube from the fluid and form a matrix out of the ...
0
votes
1answer
67 views

The divergence of the Stress Energy Tensor

I have been studying general relativity and I have often seen in textbooks that the divergence of the stress energy tensor is zero. $$T^{\mu\nu}_{;\nu} = 0$$ but is it possible to contract and ...
0
votes
1answer
112 views

Carroll's derivation of the geodesic equations [duplicate]

In Carroll's derivation of the geodesic equations (page 69, http://preposterousuniverse.com/grnotes/grnotes-three.pdf), he starts with ...
0
votes
0answers
34 views

Computer simulation/visualization of a ray of light passing near a massive object

I'd like to write a computer program that simulates and visualizes the trajectory of a ray of light as it passes near a massive object (e.g., neutron star). In other words, I'd like to model light ...
0
votes
1answer
101 views

Understanding gravitational time dilation / Schwarzschild metric

I've had a look at the answers to these sorts of questions already, but feel like I'm still missing something. Starting with this question, and this one and even this one here. I'm looking at this ...
1
vote
2answers
82 views

Can gravity be interpreted as the acceleration of spacetime towards an object? [closed]

Greetings StackExchange! We were having a conversation with a peer about stupid ways of interpreting theories. We would go to and fro with an interpretations, but we would always find a way to ...
2
votes
2answers
120 views

“Derivation” of Minkowski metric?

Is there a deeper meaning behind the the Minkowski metric? Does it just come from the SR formulae? Or is there some deeper geometrical meaning, maybe in the context of GR?
3
votes
1answer
42 views

Light trajectory

We have observed stars where "we should not" Some people say that gravity can alter light trajectory. Some people say that gravity actually alter the space on which light travels. Which one is ...
2
votes
1answer
59 views

Typical rotation speeds for black holes

I am curious as to how rapidly most black holes are spinning. A refinement of the question could be: how rapidly are typical supermassive black holes spinning? I ask because I have the impression ...
0
votes
0answers
35 views

Massive vector field in curved spacetime

Setup Consider a massive vector field in anti-de Sitter space AdS$_{d+1}$ with metric $$ ds^2=\frac{1}{z^2}\left(dx_\mu dx^\mu+dz^2\right) $$ where $dx_\mu dx^\mu$ is the line element in d+1 ...
1
vote
1answer
59 views

Time flow difference for satellites [duplicate]

Clocks in satellites have to be adjusted due to the effects of relativity; but does time for satellites (GPS) flow slower, due to the relative motion, or faster, due to the weaker amount of ...
3
votes
1answer
119 views

Why two different Lagrangians to derive geodesic equations?

I'm trying (very early stages) to understand the derivation of the geodesic equation ...
0
votes
0answers
51 views

Proof of Schwarzschild metric construction (O'neill chap 13)

I am struggling with a few steps of the proof in O'neill book $\textit{Semi-Riemannian Geometry, with applications to Relativity}$ on the construction of Schwarzschild's metric (chap13, Lemma1). Is ...
6
votes
1answer
63 views

Post-Minkowskian expansion of some quantities in Post-Newtonian theory

I'm studying Post-Newtonian theory on the book "Gravity" by Poisson and Will and I found a few formulas that I can't obtain by myself. I'm pretty sure it must be quite simple, but can't find the right ...
2
votes
3answers
96 views

Milky Way galaxy central black hole and time contraction of life story

We know that life is almost 4 billion years old on Earth. We also know that time contracts as we approach the event horizon of the massive black hole at the center of the Milky Way galaxy. Now the ...
4
votes
2answers
348 views

Age of the universe and the singularity at the Big Bang

Using the standard model of cosmology we calculate the Hubble time to obtain an estimate of the age of the universe. This model assumes a beginning of time in the past. But that point is a true ...
0
votes
1answer
33 views

Cosmology: collisionless vs collisional fluids?

I try to understand the difference between collisionless and collisional fluids in cosmology. My first question is the following. In the context of FLRW cosmology, we suppose that the Universe can ...
0
votes
2answers
157 views

Physics in the movie 'INTERSTELLAR'?

have a question , this movie is praised by the scientific accuracy however how the hell does relativity justify that the character can be thrown in black hole and survive ? also if the robot can not ...
1
vote
1answer
106 views

Why I cannot cross the Einstein-Rosen bridge?

I have been told that no observer can ever cross the wormhole present in the Kruskal-Szekeres coordinates, connecting region 1 and 4 in the Kruskal-Szekeres diagram, usually called Einstein-Rosen ...
1
vote
0answers
65 views

How does a rotating black hole look like? How would it be to descend into one?

This image from Wikipedia shows how a black hole would look like: A black circle that acts as a gravitational lens for light rays coming from behind. How would a rotating black hole look like? How ...
0
votes
0answers
40 views

How do you calculate perihelion precession in the general spherically symmetric space time?

I am trying to find the approximate solution of the differential equation obtained for the the motion of massive particle around Riessner-Nordstrom-AdS solution, equation and its solution are given in ...
0
votes
1answer
73 views

Free-falling from rest into a Kerr black hole

Is it impossible for a particle (with zero angular momentum) to free-fall from rest at infinity into the ergosphere of a Kerr black hole? It seems like it is very easy to show this is the case, but ...
-1
votes
1answer
41 views

Time dilation and biological changes

I have watched the movie Interstellar and like most of the people who watch it, I was intrigued by the effects of time travel on the astronauts. After reading some articles and watching some videos, I ...
0
votes
1answer
34 views

Does asymptotically AdS mean as $z \to 0$ or as $z \to \infty$ in Poincare metric of AdS?

The Poincare metric of AdS_3 is given by $ ds^2 = \frac{R^2}{z^2}(dz^2 - dx_0^2 + dx_1^2)$. Using the coordinate transformation $\rho = \log(z)$, we can write this as, $ds^2 = R^2 (d\rho^2 + e^{-2 ...