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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413 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: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
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1answer
192 views

Why should we believe in clock hypothesis? [closed]

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 ...
4
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1answer
278 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 ...
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0answers
94 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 ...
6
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2answers
179 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
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1answer
92 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
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1answer
430 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 ...
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2answers
1k 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 ...
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2answers
133 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
2
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1answer
92 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 ...
2
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1answer
81 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 ...
2
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1answer
108 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 ...
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0answers
36 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 ...
3
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2answers
307 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
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1answer
6k 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 ...
17
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4answers
805 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 ...
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0answers
138 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 ...
4
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2answers
175 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
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1answer
112 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 ...
5
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1answer
709 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 ...
9
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3answers
437 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
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1answer
97 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 ...
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4answers
805 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 ...
2
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1answer
115 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
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0answers
105 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 ...
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2answers
90 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 ...
2
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0answers
208 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 ...
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0answers
51 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
200 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, ...
5
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2answers
408 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 ...
5
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4answers
652 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 ...
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1answer
39 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 ...
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1answer
67 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. ...
5
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4answers
273 views

Is there a peak gravitational force between bodies?

Suppose Object A is exerting gravitational force on Object B. Object A increases in mass, and so increases in volume, increasing the gravitational force on Object B. But, since mass occupies space the ...
2
votes
1answer
37 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 ...
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2answers
34 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 ...
2
votes
3answers
192 views

Time slowed by gravity

If time moves more slowly on Earth (due to our proximity to a gravitational body) than for someone orbiting Earth in a spaceship, yet the opposite occurs in the frequently cited "twin paradox" of the ...
6
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0answers
108 views

Can some components of metric be Finslerian while the others be Riemannian?

A Finsler metric reduces to a Riemann metric in case it loses its dependence on velocities. Now, my question is this: Can we have a Finsler metric in which some components of the metric have velocity ...
5
votes
2answers
289 views

Interpreting the Kretschmann scalar

How do you interpret the Kretschmann scalar (in general relatvity)? What can you tell from it? The Kretschmann scalar is defined as $$K = R_{abcd} R^{abcd} $$ where $R_{abcd}$ is the Riemann ...
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1answer
167 views

A test for virtual particles by measuring gravity fluctuations possible?

Ok to begin I will begin by talking briefly about my discussions with my Quantum Mechanics (specializes in Particle physics) professor and my Cosmology Professor (who studies particle physics with ...
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2answers
274 views

Is four-current a vector or a vector density?

According to MTW, $$F^{\alpha\beta}{}_{;\beta} = 4\pi J^\alpha$$ and we can infer that the four-current must be an ordinary vector field because the left side is tensorial. But Wikipedia says that ...
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1answer
69 views

In general relativity, do light/time behave as in free space if the net force of gravity is zero?

If photons/particles are on lines equidistant from two bodies of mass, does time look the same to them as it would without the bodies of mass? Or is time slowed regardless? (Given massive bodies $a$ ...
2
votes
1answer
251 views

Can I practically demonstrate Gravitational Time Dilation by spinning a wheel very fast? [duplicate]

In an attempt to demonstrate gravitational time dilation, I was curious if it were practical to mount a clock to a fast spinning wheel, with the centripetal acceleration of the wheel being equivalent ...
2
votes
1answer
133 views

The relationship between the structure of spacetime and the existence of spinor field?

We all know that the existence of spinor fields implies that spacetime must be time-orientable. Thus that spacetime is time-orientable is a necessary condition for existence of spinor fields. Geroch, ...
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votes
1answer
60 views

If you are not given a metric, which one is more fundamental: a vector or a covector? [closed]

If we do not have the metric $g_{\mu\nu}$ for a given spacetime, are vectors $x^\mu$ more fundamental than covectors $x_\mu$ or vice versa? Why? (if the metric were given we could just raise/lower ...
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2answers
74 views

Gravitational force of several massive bodies, from the viewpoint of general relativity

According to Wald's GR, "absolute gravitation force has no meaning". The text goes on to describe two cases: one where a gravitational force can be defined, and one in which it cannot. I'd like to ...
2
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0answers
241 views

Computing the Ricci Tensor for a Spherically Symmetric Spacetime

For a homework question, we are given the metric $$ds^2=dt^2-\frac{2m}{F}dr^2-F^2d\Omega^2\ ,$$ where F is some nasty function of $r$ and $t$. We're asked to then show that this satisfies the Field ...
2
votes
1answer
416 views

Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= ...
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7answers
5k views

Why does rotation simulate gravity if motion is relative?

In Einstein's theory of relativity, if motion is truly relative, then why would somebody in a rotating space station experience (artificial) gravity? I mean, I get why they experience gravity IF the ...
2
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0answers
93 views

Can a gravitational wave produce oscillating time dilation?

I was reading about gravitational waves and about laser based detectors. I also read this. As mentioned in the answer, when ever there is a deformation in spacetime, doesn't it also create a minute ...