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.

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Does the gravitational force of a massive, spherical body draw only towards its center of gravity, and to no other area?

Consider the premise that at the center of Earth (for example) an object would be weightless because of the relatively even distribution of mass surrounding it, and the resulting gravitational pull on ...
0
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3answers
33 views

Proving a relation with Four-velocity tensor [duplicate]

I'm trying to show that: $U^a_{\space\space;b}U^bU_a = 0$ (Where U is four-velocity) and I'm stuck on how to go about it. I tried expanding it out into the Christoffel symbols, but that didn't seem ...
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1answer
56 views

Why is it hard to detect a black hole

I've read in some texts that we can't directly observe a black hole in space because not even light can escape from it's gravity. Some of the indirect observational methods mentioned are, ...
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2answers
117 views

Can gravitational waves escape from inside of black holes? [duplicate]

I understand that light cannot escape from inside of an event horizon because the spacetime curvature is too warped for photons to escape. On the other hand, gravitational waves are ripples of ...
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0answers
35 views

How can I find a numerical solution for Einstein's field equation?

If I am given accurate measurements for the mass of an object how would I go about finding numerical solutions for Einstein's field equation? Would I start by solving Newton's equation for a large ...
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0answers
21 views

Which manifold spacetime really is? [duplicate]

There exists many different manifolds with many different topologies and smooth structure out there. There the euclidean spaces $\mathbb{R}^n$, the spheres $S^n$, and many other possible examples. ...
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1answer
42 views

Effect of a rotating disk on a grandfather clock

The question is as follows: A grandfather clock is placed on a rotating disk. Given the disk rotates once every minute, how long does it take for the clock to be one second out? Am I correct in ...
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0answers
11 views

Schwarzschild radius after inflation [duplicate]

if after inflation the universe was only a fraction of a centimeter, all matter (or its energy equivalent) would be contained within that small volume. If I apply General Relativity (GR), (unless I ...
2
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2answers
274 views

Finding the metric tensor from the Einstein field equation?

I have have set my self a challenge to learn all the maths behind the Einstein field equation (EFE), and from reading it seems that the Metric tensor is the thing we are trying to find (from the 10 ...
8
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3answers
120 views

Why doesn't $ds^2 = 0$ imply two distinct points $p$ and $p'$ on a manifold are the same point?

Let's suppose I have a spacetime manifold $M$. Let $p$ be a point on my manifold. Now I move from $p$ to some other point $p'$. Presumably I should have moved some "distance" right? How can I speak of ...
9
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2answers
293 views

The Aharonov-Bohm effect is purely classical, right?

Every discussion I've ever seen of the Aharonov-Bohm effect makes a big deal of its being a quantum effect with no classical analogue. But as far as I can tell it is present already at the classical ...
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1answer
45 views

Does anyone recognize the line element $ds^2 = ( 1 - \frac{2m}{r} )dt^2 + 2 dt dr$?

I've stumbled upon the line element $ds^2 = ( 1 - \frac{2m}{r} )dt^2 + 2 dt dr$. Obviously the corresponding metric tensor has components: $\begin{bmatrix} g_{tt} & g_{tr} \\ g_{rt} & g_{rr} ...
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2answers
54 views

Proper length in GR

What meaning/use is associated with the notion of proper length in general relativity? Do you know an example of any quantity that depends on it? I have so far found statements like "the length ...
3
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2answers
84 views

How does one calculate the full perihelion shift of Mercury, including perturbations from other planets?

I'm talking about the full calculation, including perturbations from other planets. I've seen the general relativistic correction done a half dozen times before, but I can't say that I've seen the ...
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0answers
19 views

The limited computing capacities of space lead to time-dilation near mass and with movement? [on hold]

Has anyone tried to approach physics using space as a computing medium? It seems like a lot of things could be explained with this approach. With the acceleration of the expansion of the universe as a ...
3
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1answer
64 views

Are all reference frames equally valid?

Are accelerated reference frames as valid / real as inertial frames, or are accelerated frames a convenience of integrating across a continuum of inertial frames? For instance, it makes sense to ...
4
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1answer
457 views

Step by step algorithm to solve Einstein's equations

I cannot completely understand what is a regular method to solve Einstein's equations in GR when there are no handy hints like spherical symmetry or time-independence. E.g. how can one derive ...
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3answers
352 views

Einstein tensor in Friedmann equations : where is the missing $c^2$?

I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere. In all the following $\rho$ ...
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4answers
92 views

What is the meaning of Einstein's field equation in terms of source and its effects on curvature?

The Einstein's Field Equation is $$R_{\mu\nu}-(1/2)g_{\mu\nu}R=-8\pi T_{\mu\nu},$$ where the left hand side is the curvature term and the right hand side is the source term (see, Hartle). Now, in the ...
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0answers
75 views

Questions about “geodesic path” and “arc length of a geodesic path” in the context of GTR and “Lorentzian manifolds”

I'd like to check my understanding of the notions "geodesic path" and "arc length of a geodesic path" in the context of GTR and "Lorentzian manifolds". Considering a set of "spacetime events", ...
1
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1answer
56 views

How can I use Einstein's field equations to find the metric tensor? [duplicate]

I have watched and read a lot on the topic of General Relativity and the geometry behind it. I am confident that I can derive an approximation of the the stress-energy-momentum tensor with just the ...
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4answers
670 views

Event horizons without singularities

Someone answered this question by saying that black hole entropy conditions and no-hair theorems are asymptotic in nature -- the equations give an ideal solution which is approached quickly but never ...
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1answer
81 views

What is the covariant basis around a Schwarzschild black hole?

First of all, I'm not interested in time for this question. So lets consider a 3-manifold whose metric is the spatial part of the Schwarzschild metric, so it has the event horizon and the singularity ...
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0answers
31 views

The limited Computing Capabilities of Space, Increased quantized info leads to time-dilation?

Are there any approaches to Special and General Relativity using space as a computing medium? With space having a maximum computing capability and time dilation as lag? Could this idea describe the ...
1
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1answer
269 views

Questions about MTW's “thousand” tests of the Einstein principle

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
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1answer
76 views

Why is space (almost) flat? Is it because masses are approximately homogeneously distributed? [duplicate]

The question I have is: Why is space (almost perfectly) flat in our neighbourhood? (I am disregarding the deviations due to the sun and the planets.) Is it correct to say that space is (almost) flat ...
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0answers
38 views

How does Einstein's gravity work? [duplicate]

I'm a chemistry student interested in physics. Hope the question doesn't sound funny. As opposed to Newton's gravity, which doesn't explain how gravity works, Einstein explained gravity as a result ...
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3answers
148 views

Finding the appropriate coordinate transformation given two metrics

Given the two-dimensional metric $$ds^2=-r^2dt^2+dr^2$$ How can I find a coordinate transformation such that this metric reduces to the two-dimensional Minkowski metric? I know that ...
3
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1answer
90 views

Is any spacetime metric physically realizable?

Given a spacetime metric, you could work out a stress-energy tensor for each position that would result in that metric. I know building a wormhole requires negative energy densities, which are ...
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0answers
19 views

Free Components of the Riemann Tensor

Knowing the symmetries of the Riemann tensor, it is known that in 4-dimensional space we would have only 20 free components. My question is: How one can decide which components are necessary to ...
0
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1answer
47 views

Will a stress-energy tensor have the same identities as it's metric?

Say I have a metric tensor where $$g_{00} = -c^{2}\ and $$ $$g_{01}=g_{02}=g_{03}=0$$ and $$g_{12}=g_{13}=g_{23}$$ and $$g_{11}=g_{22}=g_{33}$$ My question is straightforward: would the same or ...
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0answers
40 views

Can it happen that in less gravity clock goes slower but the actual time remain same? [closed]

It is said that clock in satellite goes slower than that on Earth because of time dilation .(by 'clock' I mean the mechanical instrument that measures time)
2
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1answer
130 views

Is my diagram of spacetime curvature valid (relatively)?

I've been wracking my brain trying to understand what "curved spacetime" really is, and I think replacing one dimension with the time dimension then drawing the world-lines through time was the "aha!" ...
2
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4answers
140 views

Are empty black holes possible

When just considering GR without evaporation nor QM, is an empty (containing no matter or anything) black hole possible ? Let's say that there is only GR and nothing else (no matter or boson fields), ...
2
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1answer
97 views

Calculate the mass of a Schwarzchild black hole with Komar integral

In Wald's GR, Komar integral is Eq. (11.2.9): $$M=-\frac{1}{8\pi}\int_S\epsilon_{abcd}\nabla^c\xi^d$$ $S$ can be chosen as a 2-sphere, the boundary of a spacelike hypersurface $\Sigma$ such that the ...
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2answers
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Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness?

Can anyone please explain Hawking-Penrose Singularity Theorems and geodesic incompleteness? In easy to understand plain English please.
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0answers
53 views

Newtonian oscillator in a box [on hold]

To help me understand relativistic momentum and gravity effects, I would like comments on this artificial example. Inside a box, two equal masses m are connected by an ideal spring and allowed to ...
3
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1answer
47 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
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1answer
67 views

$U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
0
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1answer
57 views

Time dilation as an effect of energy density

Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation? i.e. Higher energy density==>Slower rate of time?
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3answers
237 views

Gravity on the International Space Station - General Relativity perspective

My question is an extension to this one: Gravity on the International Space Station. If all the outside views of the ISS was sealed, then the crew inside would not be able to tell whether they were ...
3
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3answers
163 views

Is the accelerated expansion of the universe consistent with conservation of energy? [duplicate]

If energy can neither be created nor destroyed, how come the universe is expanding at an accelerating rate? Where does this energy come from?
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2answers
58 views

Bending of space vs. bending of a body - which is larger, and by what factor?

This is not homework, but is a problem I am asking myself. A long rod with known elastic material properties floats in flat space - suspended and kept in place by a number of massless ropes. Now we ...
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2answers
34 views

Does the value of the Ricci scalar determine the strength of the gravitational field?

If I was solving an equation that contains the Ricci Scalar, and I want to solve the equation in the strong and weak gravity regimes, is right to assume that $R>>1$ for first case and ...
4
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2answers
215 views

Gravitational waves as information carriers

Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?
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2answers
46 views

Michelson & Morley

I KNOW this is a common question in it's topic, but not in this form.. I'm reading a book which explains the significance of certain aspects of experiments.. This section is called "null ...
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2answers
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Is there a limit as to how fast a black hole can grow?

Astronomers find ancient black hole 12 billion times the size of the Sun. According to the article above, we observe this supermassive black hole as it was 900 million years after the formation of ...
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1answer
48 views

The einbein in the action of a relativistic massive point particles [closed]

The action of a relativistic massive point particle moving in space-time is $$S=-m\int d\tau \sqrt{g _{\nu \rho}\frac{dx^{\nu}}{d\tau}\frac{dx^{\rho}}{d\tau}}$$ [with Minkowski sign convention ...
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3answers
326 views

Given the Wikipedia notion of “arc length”, how is its manifestly real “signed variant” to be called and denoted?

I am dissatisfied with the presentation (not to say "definition") of "arc length", in its "Generalization to (pseudo-)Riemannian manifolds", as given in Wikipedia. (Who isn't?. But I'll sketch it here ...
0
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1answer
31 views

Energy variations of cosmic background radiation

Has anyone been able to measure a difference in the energy density of Cosmic Background Radiation in a gravity well compared to zero gravity?