A theory that describes how matter produces and responds to 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)

2
votes
0answers
34 views

Time functions in general relativity

In my general relativity notes a function $f$ is called time function, if $\nabla f$ is time-like past-pointing. Say that we are in Schwarzschild spacetime and I want to check if $f=t$ is a time ...
1
vote
3answers
44 views

Gravitational time dilation, does time of the observer at a lower gravitational potential looked slowed down in the frame of the higher one

This question is mainly inspired after watching the movie known as Interstellar We knew that for time dilation caused by relativistic motion between A and B. A will measure B's clocks slowing down, ...
-2
votes
1answer
74 views

Questioning Einstein's view on gravity [duplicate]

Oke, so my mind is blown by Einsteins view on gravity, at least as far as I understand the basics and principles he based his views on. One of the first things that struck me was that most of his ...
14
votes
2answers
2k views

Why don't we have a theory of everything?

What is currently stopping us from having a theory of everything? I.e. what mathematical barriers, or others, are stopping us from unifying GR and QM? I have read that string theory is a means to ...
0
votes
1answer
59 views

Can Einstein's 'Theory of General Relativity' exist in Harmony with 'Quantum Mechanics'? [on hold]

From the Book 'In Search of Schrodinger's Cat': Coordinates in space-time represent position; causality depends on knowing precisely where things are going, essentially on knowing their momentum. ...
12
votes
3answers
837 views

What is the most compelling evidence of General Relativity in the presence of matter and energy?

The most oft-cited triumphs of GR are things such as the shifting perihelion of Mercury, gravitational redshift experiments, and gravitational lensing. But, as far as I know, these are only ...
4
votes
3answers
84 views

Is gravitational Chern-Simons action “topological” or not?

Here are the 2+1D gravitational Chern-Simons action of the connection $\Gamma$ or spin-connection: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
0
votes
1answer
128 views

Why should we believe in clock hypothesis?

It is often assumed in special relativity that the rate of a clock in a non inertial frame does not depend on the proper acceleration of the observer. The point is, Rindler's observer shows us that ...
0
votes
0answers
22 views

Ricci tensor of schwarzschild metric [on hold]

In schwarzschild metric: $$ds^2 = e^{v}dt^2 - e^{u}dr^2 - r^2(d\theta^2 +sin^2\theta d\phi^2)$$ where $v$ and $u$ are functions of r only when we calculate the Ricci tensor $R_{\mu\nu}$ the non ...
4
votes
1answer
65 views

Conformal Killing fields on Schwarzschild

I am trying to understand which are the conformal Killing Fields on the Schwarzschild spacetime. I say that $X$ is a conformal Killing field on $S$ ($S$ is Schwarzschild) if there exists a function ...
0
votes
0answers
47 views

Is it possible to assign a physical radius to a black hole?

The Schwarzschild metric is given by: $$c^2d\tau^2 = \left(1-\frac{r_s}{r}\right)c^2 dt^2-\left(1-\frac{r_s}{r}\right)^{-1}dr^2 - r^2 \left(d\theta^2 + \sin^2 \theta \, d\varphi^2\right).$$ The ...
5
votes
2answers
140 views

Akin to gauge field, why GR's lagrangian is not $R_{abcd}R^{abcd}$? What's the mathematical or physical meaning of $R_{abcd}R^{abcd}$?

For gauge field theory, the Lagrangian of the gauge field is $$\mathcal{L}=-\frac{1}{4}\mathrm{tr}(\mathcal{F}_{\mu\nu}\mathcal{F}^{\mu\nu})=-\frac{1}{8}F_{a\ \mu\nu}F^{a \ \mu\nu}$$ The field ...
3
votes
1answer
52 views

Why do we need frame-fields to describe fermions in SUGRA?

I'm learning about the frame formalism and read that to couple fermions to gravity you need to go to the frame-formalism. As a motivation to learn more about frame-fields would someone sketch me why ...
4
votes
1answer
125 views

What would happen if a negative mass crossed the event horizon of a black hole?

If negative mass really existed and somehow a very fast traveling negative mass object reached near the black hole's event horizon. What would happen when it crosses the event horizon? According to ...
0
votes
2answers
82 views

How does covariant derivative act on Christoffel Symbols?

the question is how the covariant derivative acts on the following? $\nabla_\nu(\Gamma^\alpha_{\mu\lambda}R^{\beta\lambda})=?$ and ...
0
votes
1answer
53 views

How are these types of time dilation related?

How are these two phenomena related (if at all): 1. Gravitation slowing down time 2. High speed slowing down time
3
votes
0answers
62 views

A proof for Newtonian origin of residual perihelion advances in solar system

In an Amazon book it is given a very simple formula $$\delta = \frac{k}{T^{5/3}}$$ conforming to which the so-called residual advance of perihelion $\delta$ of each inner planet in solar system ...
2
votes
1answer
42 views

Does inflation predict a closed universe?

I read somewhere that both a closed and a finite flat universe would have zero total energy in General Relativity (On the Zero-Energy Universe). But the best evidence shows that the universe is flat ...
3
votes
1answer
57 views

Effect of cosmological constant on time

The cosmological constant is introduced in Einstein equations in the form : $G_{\mu\nu} = T_{\mu\nu} + \Lambda g_{\mu\nu}$, as I understand it, shouldn't the term $\Lambda g_{\mu\nu}$ have effects on ...
0
votes
0answers
50 views

Discontinuous momentum in relativity

I'm thinking about a fantastical scenario where the velocity of all macroscopic objects in the universe is instantaneously set to 0. In a Newtonian reference frame, this is relatively easy to ...
1
vote
1answer
31 views

Are quantum-entangled particles affected by relativistic speeds? [duplicate]

In my answer to a recent question on World Building, I suggested that quantum-entangled particles would be a good way for ships traveling at relativistic speeds to communicate. My understanding is ...
1
vote
1answer
48 views

Length contraction, front middle or back

I still don't have a solid understanding of Length contraction. Imagine we have a ruler of length $L$ that starts at rest upon a ground with markings on it, then accelerates until nearly the speed of ...
0
votes
0answers
29 views

Does a body curve spacetime at higher velocities? [duplicate]

Suppose we have two objects where the distance over time decreases. Now, as I understand it, general relativity says that we can observe the Universe from the perspective of both objects an get a ...
2
votes
1answer
69 views

From affine space to a manifold?

One of the several definitions of an affine space goes like this. Let $M$ be an arbitrary set whose elements are called points, let $\mathcal{V}$ be a vector space of dimension $n$, and let ...
1
vote
1answer
108 views

Time dilation - Earth & Jupiter [duplicate]

I have this doubt after watching Interstellar movie :) Lets assume I am in Jupiter. (I know it is a gas planet, full of hydrogen and helium, has extreme pressure etc. Lets please ignore those facts ...
0
votes
0answers
26 views

Relative time dilation in Schwarzschild metric

Let's say we use the Schwarzschild metric to model the curved spacetime around a planet of mass $M$ and radius $R_0$. One clock $A$ is hovering at distance $R_A$ > $R_0$ with the help of rockets, a ...
0
votes
0answers
49 views

Coordinate Symbol confusion in general relativity

In a previous post (Finding the metric tensor from the Einstein field equation?), the equation used lambda, rho mu and nu (not sure of the names of the letters!) for the Ricci tensor and swapped to a, ...
4
votes
0answers
63 views

Interpretation of a singular metric

I'm interested to find out if we can say anything useful about spacetime at the singularity in the FLRW metric that occurs at $t = 0$. If I understand correctly, the FLRW spacetime is a combination ...
1
vote
0answers
59 views

Manifold for Schwarzschild and Bertotti-Robinson

In short: what is the manifold in discussion for Schwarzschild metric $$ ds^2 = -(1-\frac {2M}r)dt^2 + \frac1{1-\frac{2M}r} dr^2 + r^2 (d\theta^2 + \sin^2 \theta d\phi^2)$$ and Bertotti-Robinson ...
3
votes
1answer
72 views

How close can an observer approach the black hole in an unpowered flyby without falling into it?

In classical mechanics by choosing the right trajectory you can approach a planet arbitrarily closely, if there is no atmosphere or anything to slow you down, you can approach the surface then fly ...
2
votes
1answer
49 views

Integration and Differentiation of Proper Time

My question concerns the general relativity setting. Integration: Proper time is defined by $$\tau = \int_P\sqrt{g_{\mu\nu}dx^\mu dx^\nu}$$ but happens when $g_{\mu\nu}\neq 0$ for $\mu\neq \nu$ ? For ...
3
votes
1answer
582 views

Gravity is curved geometry: A fact of nature or model-dependent interpretation?

We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by ...
0
votes
0answers
25 views

Using Special Relativity in Uniform Circular Motion [duplicate]

Can one utilize the formulas of Special Relativity in uniform circular motion? The radial component of the object does accelerate, but sometimes we are just interested in its tangential speed. Here ...
10
votes
3answers
310 views

Entire Universe's Momentum

I was thinking about the definition of the conservation of momentum, which says that momentum is conserved unless outside forces are acting on the system, and I was wondering that if the system is the ...
0
votes
1answer
68 views

Are Asimov's short duration spacetime “jumps” feasible? [closed]

In books of science fiction (Asimov) I saw the fancy idea of a "jump" over a space-time interval, (i.e. at superluminal velocity and for a VERY SHORT time). The result was landing in another region of ...
12
votes
3answers
551 views

Coulomb's Law in the presence of a strong gravitational field

I was under the impression that the $1/r^2$ falloff of various forces were because of the way the area of a expanding sphere scales. But that strict $1/r^2$ falloff would only be globally true in a ...
1
vote
1answer
65 views

Non-geodesic circular orbit? [closed]

From N. Straumann, General Relativity Exercise 4.9: Calculate the radial acceleration for a non-geodesic circular orbit in the Schwarzschild spacetime. Show that this becomes positive for ...
3
votes
0answers
60 views

Is the metric-induced topology relevant at all in a (psuedo) Riemannian manifold? [duplicate]

A (pseudo) Riemannian manifold is a tuple: $$(M,g)$$ where $M$ is a smooth manifold (in particular, a topological space with an atlas) and $g$ is a (pseudo) Riemannian metric tensor. It is apparent ...
1
vote
2answers
65 views

Can Einstein's constant explain expansion?

I read somewhere that Einstein or Newton believed that the universe was completely static, where it neither expanded nor contracted, but simply remained fixed. It was concluded that due to attraction ...
1
vote
0answers
36 views

Free fall coordinates/Fermi (normal) coordinates

It makes sense intuitively given the equivalent principle, and I've seen many times it stated, that for a free fall (geodesic) path in an arbitrary spacetime, we can choose our coordinate system to ...
0
votes
0answers
31 views

How does an observer in arbitrary state of motion assign numbers to events in a flat spacetime?

In a flat spacetime, there is an inertial observer, who assigns events coordinates in a usual fashion: Placing a clock everywhere and synchronize them. From his POV, the other observer is moving in ...
3
votes
1answer
103 views

Time derivative of time-translation Killing vector

I'm working with the spherically symmetric, static black hole metric. In the problem I'm working on, I'm told that $K$ is the time-translation Killing vector, $\frac{\partial}{\partial t}$ or $K = (1, ...
0
votes
0answers
140 views

Time Dilation Geometry

I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing ...
5
votes
2answers
199 views

Spacetime diagram of a collapse of a rotating star

There is a well-known "standard" spacetime diagram (Kruskal and Penrose) for the collapse of a spherically symmetric star to a Schwarzschild black hole (for example here, or here in EF), which stands ...
3
votes
3answers
82 views

Derivation of Kerr metric, is there any reference?

In studying general relativity, many text deals with the derivation of Schwarzschild metric starting from generic metric form. After that impose static, spherical symmetry and obtain the desired ...
0
votes
1answer
25 views

Why is $p\cdot u_{\mathrm{obs}} = -E$ valid in curved spacetime for a stationary observer?

An observer stationed at a fixed Schwarzschild radial coordinate R near a spherical star of mass M observes a photon moving radially away from the star and measures its energy to be E. What are the ...
1
vote
1answer
31 views

A particular coordinate transformation of a metric tensor

So, this was a problem set question for my GR class due yesterday, and I can't for the life of me solve it, it seems I am missing something very trivial. Either the given answer is wrong, or I am. ...
2
votes
1answer
30 views

Different between $\mu$ and $T_{00}$ in perfect fluid solutions?

In the perfect fluid solution for general relativity, you get $$T_{ab} = u_a u_b (\mu + p) - g_{ab} \, p$$ I've seen varying descriptions of what $\mu$ is, and some places describe it as the local ...
0
votes
2answers
22 views

entropy-infomartion correlation at preliminary universe?

according to the theory of cosmic inflation after Alan Guth, the information should have travelled 100 times the speed of light at the very beginning after the big bang. -when we talk about ...