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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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 ...
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76 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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40 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 ...
7
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3answers
201 views

Is every spacetime metric physically realizable?

Is every spacetime metric physically realizable? I know that given any spacetime metric, you could work out a stress-energy tensor for each position that would result in that metric. However, I also ...
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0answers
26 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 ...
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3answers
243 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 ...
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1answer
99 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 ...
2
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1answer
163 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!" ...
3
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1answer
156 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 ...
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1answer
86 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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63 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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175 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), ...
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160 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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1answer
99 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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2answers
57 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 ...
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2answers
60 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 ...
0
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1answer
113 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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2answers
2k views

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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3answers
241 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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1answer
39 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?
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63 views

Are there experimentally verified differences between general relativity and Lorentz invariant “newtonian” gravity?

I used to have (I lost it) a historical article about how Eintein's general relativity theory "won" over a Lorentz invariant generalization of Newton's gravity (I cannot remember the author). This is ...
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0answers
39 views

Infinite universe, big bang = no singularity? [duplicate]

If we traced an infinite universe back in time towards t=0(ish) would a singularity still be formed? Would the singularity be infinite in size? (To me it seems it would have to be) This reminds me ...
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2answers
139 views

What is the speed of light after it has entered a black hole?

I was just thinking about this the other day. Given Einstein's Relativity etc. assigning the cosmic "speed limit" the value of $c=299792458\:\frac{m}{s}$, we know that the event horizon is the point ...
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1answer
58 views

Does GR reflect Aristotelian time?

This is really a philosophical question, which I've already asked at Phil.SE but I'm asking here with more physics detail. In Newtonian Mechanics, space and time are independent of each other, and of ...
0
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1answer
111 views

Is there any paper analyzing the validity of Relativity in expanding space? [duplicate]

Big Bang models result from applying Relativity equations to expanding space; however, as Einstein noted, Relativity was not established in expanding space. A basic question arises: is Relativity ...
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49 views

How can spacetime affect massless entities? [duplicate]

Why is light affected and "bent" by spacetime if it has no mass or density?
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183 views

Can a sufficiently large black hole be singularity-free?

This came to me after reading that a black-hole that has the mass of the observable universe will also have an event horizon that covers the observable universe. Since the definition of a black hole ...
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1answer
84 views

Geodesic equation

I have a technical question about the geodesic equation. Assume we have a frame $(E_{1},E_{2},E_{3},E_{4})$ (not necessarily a coordinate frame). Assume we have a parametrized curve $\gamma(s)\in M$ ...
3
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1answer
70 views

What is a nongeodesic orbit?

I have read that in the Schwarzschild spacetime for a nongeodesic circular orbit the radial acceleration becomes positive for $r<3r_S$. Intuitively, the acceleration should be negative, pulling the ...
3
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3answers
145 views

Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?

IIs it valid to apply Einstein's Relativity to scenarios involving expansion of space? For a practical example of this: Is it legitimate to speak of distant red-shift galaxies as experiencing time ...
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1answer
114 views

Aether atmospheres

http://arxiv.org/abs/1004.1467 claims to have an alternative explanation of the interaction of light around massive objects. Many of the general-relativity-tests such as bending of light near a ...
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3answers
362 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 ...
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1answer
123 views

Why does the electric field escape a black hole? [duplicate]

An (unlikely) charged black hole can be described with the mass, angular momentum, charge and the thermal radiation. The reasoning behind the thermal radiation rests on the particle creation outside ...
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97 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", ...
3
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1answer
237 views

Dirac operator in curved spacetime in 2 dimensions – hermitian?

I'm currently trying to learn about the Dirac equation in curved spacetime and have come across an odd remark in Nakahara's well-known textbook "Geometry, Topology and Physics" that I would like to ...
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126 views

Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
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2answers
75 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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1answer
90 views

Different forms of the Einstein field equation

I am working my way through the wonderfully written introduction "General relativity for mathematicians" by Sachs & Wu. I am indeed a mathematics student and find this book to be well suited to ...
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0answers
99 views

Do past and future exist? [closed]

Ok, first thing I want to say is that I'm a layman. No high school math background whatsoever, so I'd be greatful if you could provide an explanation without equations. Now I'm quite interested in ...
0
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1answer
56 views

Energy-Momentum Tensor with mixed indices

I know that $T_{\mu\nu}$ is the Energy-Momentum Tensor and $T=g^{\mu\nu}T_{\mu\nu}$, but does anyone know what $T^{\nu}_{\mu}$ is and how its calculated?
2
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2answers
138 views

Gravity as a particle-based force vs space-time warp

I'm interested to understand the interpretation of gravity as a result of exchange of force particles (ie gravitons) vs General Relativity-based warping of space-time. Related to this is while a ...
2
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1answer
179 views

Inverse Metric Tensor

First the setup: Let $\mathcal M$ be a $2$-dimensional manifold. Let $U_P$ be some open neighbourhood of a point $P \in \mathcal M$. Let $\mathcal F : U_P \rightarrow \mathbb R \times \mathbb R$ be ...
2
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1answer
93 views

Fastest way to find the curvature terms from a given metric [closed]

I want to find the spherically symmetric, static solutions to Einstein's equations $$ R_{\mu \nu} - \frac{1}{2}Rg_{\mu \nu} = 0 $$ in four dimensions using the metric $$ g_{\mu \nu}dx^{\mu}dx^{\nu} ...
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1answer
40 views

Calculation, radius of Saggriatus A* (SMBH) , Error in Wikipedia?

The parameter Schwarzschild Radius of Saggriatus A* is given in Wiki by 2.08×1015 (~0.2 ly) see in Parameters http://en.wikipedia.org/wiki/Schwarzschild_radius However, when I do the calculation ...
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2answers
95 views

If a theory gets two predictions right, how likely it is that the rest of the predictions are true too? [closed]

The question lucidly defines what I am trying to inquire, so there is no need to elucidate it any further. Another question would be, General/Special Relativity has gotten some predictions right as ...
13
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2answers
2k views

Why is spacetime not Riemannian?

I apologize if this is a naïve question. I'm a mathematician with, essentially, no upper-level physics knowledge. From the little I've read, it seems that spacetime is Lorentzian. Unfortunately, the ...
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1answer
67 views

Simple question about the electromagnetic tensor written as a 2-form

I noticed that the 2 form (Electromagnetic tensor) is written as: $$F= F^{ab}e^a \wedge e^b$$ while we know that $$F= F_{\mu\nu}dx^\mu \wedge dx^\nu$$ Is there something wrong with the indices ...
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72 views

Topology of a black hole

How many dimensions are theorized for a black hole, in view of the fact that black holes are not observed directly.
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44 views

For gravitational wave from twin stars, how was the tidal effect counted?

As the primary indirect evidence, the work on calculating the rotational slow down earned the 1993 Nobel prize. However, I cannot find any where mention how the work deal with the tidal effect. Are ...
3
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1answer
284 views

Is dark energy around a black hole locally curved?

The repartition of dark energy in the vacuum is homogeneous all over the universe. The diagram below represents space with a black hole in the middle. The square is divided in small unit squares. If ...