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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108 views
Are electrons moving? If so relative to whom? and why is there no magnetic field?
electrons on earth moving with us, due to rotation of earth, revolution of earth, sun and our galaxy right?
Then, why is there no magnetic field around a piece of copper wire?
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0answers
50 views
Second order action ADM formalism
I am trying to derive the second order action
$$S_{(2)}~=~\frac{m_{pl}^{2}}{8}\int a^{2}[(h_{ij}')^{2}-(\partial_{i}h_{ij})^{2}]d^{4}x, $$
used for tensor fluctuations derived from the ADM ...
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2answers
89 views
Gravitational distortion of an object's diameter, at a distance,
Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?
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0answers
44 views
does a rotating moving body in “flat” space curve its path because of frame dragging?
I am not a physicist.
let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible.
let's say the ...
2
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0answers
72 views
Fermi Walker vs. Fermi transport
A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
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1answer
87 views
General Relativity Paradox - Different local times of two frames a constant distance apart
Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A.
...
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109 views
Going through a ring of black holes
Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right.
Suppose one finds, or builds, a constellation of several black holes arranged in a circle. ...
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24 views
Why photons can't escape black hole? [duplicate]
Photons do not have (rest) mass. Then why are they attracted by the black hole? And is it possible that a photon crossing a black hole from a little distance could get accelerated due to the force?
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45 views
Trying to speak correctly of spacetime intervals and how to compare them
Is it correct to speak of "magnitude of a spacetime interval"?
For instance, considering a pair of (distinct) events, $A$ and $B$, which are lightlike separated, is it correct to say that "the ...
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2answers
323 views
The Uncertainty Principle and Black Holes
What are the consequences of applying the uncertainty principle to black holes?
Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
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2answers
631 views
Did Hilbert publish general relativity field equation before Einstein?
Did Hilbert publish general relativity field equation before Einstein?
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1answer
153 views
Calculating Riemann Tensor Using Tetrad Formalism
I was trying to calculate the Riemann Tensor for a spherically symmetric metric:
$ds^2=e^{2a(r)}dt^2-[e^{2b(r)}dr^2+r^2d\Omega^2]$
I chose the to use the tetrad basis:
$u^t=e^{a(r)}dt;\, ...
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1answer
50 views
Regarding Electromagnetic Plane and Maxwell equations
I asked this on the math.stackechange but I was told that it might be a good idea to ask here too since my problem is physics/math! Here is the question:
Hello everybody I am kind of struggling with ...
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1answer
141 views
Does the curvature of space-time cause objects to look smaller than they really are?
What's the difference between looking at a star from a black hole and looking at it from empty space?
My guess is that the curvature of space-time distorts the wavelength of light thus changing the ...
2
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0answers
89 views
Falling into a black hole emitter vs observer
Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole.
Suppose we define the quantity $$u=t- v$$ where $$dv/dr= ...
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1answer
92 views
Understanding how the rate of time changes
The rate at which time passes is relative depending on speed and the gravity as predicted in general relativity. This theory has been tested by scientists by comparing two identical atomic clocks, one ...
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73 views
Einstein +Maxwell 's tensor
Why is it true that we can deduce that Einstein's GR equations coupled with Maxwell's EM equations may be written in the form $$R_{ij}=C(F_{ik}F_j^{\,\,k}-{1\over 4}g_{ij}F_{mn}F^{mn})$$
without ...
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1answer
92 views
Liouville's theorem and gravitationally deflected lightpaths
It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane.
Then, ...
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1answer
77 views
Spacelike slicing of Schwarzschild geometry
I am having trouble understanding how to obtain a spacelike slicing of the Schwarchild black hole. I understand there is not a globally well defined timelike killing vector, so we can define t=cte ...
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3answers
114 views
Relation between the determinants of metric tensors
Recently I have started to study the classical theory of gravity. In Landau, Classical Theory of Field, paragraph 84 ("Distances and time intervals") , it is written
We also state that the ...
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2answers
71 views
Why can certain functions be absorbed into the Schwarzschild metric, while others can't?
Another question about the Schwarzschild solution of General Relativity:
In the derivation (shown below) of the Schwarzschild metric from the vacuum Einstein Equation, at the step marked "HERE," we ...
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1answer
260 views
Gravitational Redshift around a Schwarzschild Black Hole
Let's say that I'm hovering in a rocket at constant spatial coordinates outside a Schwarzschild black hole.
I drop a bulb into the black hole, and it emits some light at a distance of $r_e$ from the ...
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2answers
241 views
Einstein Field Equations and Electromagnetic Stress-Energy Tensor
My question is: if we write Einstein field equations in this form:
$$R_{\mu\nu} - \dfrac{1}{2}g_{\mu\nu}R=8\pi \dfrac{G}{c^4}T_{\mu\nu}$$
Then the left hand side is one statement about the geometry ...
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3answers
146 views
General Relativity Equivalence
Is Einsteins Equivalence theorem in General Relativity correct? It seems to me that it neglects the fact that gravitational acceleration depends upon separation distance squared, thus neglecting the ...
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1answer
81 views
How to choose a solution from all possible solutions of general relativity
So there are so many solutions for general relativity - then how does one "choose" the solution that is right one? By checking with observation? (though I also know that it is currently unknown which ...
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2answers
89 views
Does the distance to the cosmic horizon Lorentz-contract? Does the universe Lorentz-contract?
Our universe has a finite size. It is often called the "radius of the universe", or "distance of the cosmic horizon".
If we would fly with relativistic speed at the position of our Earth, would this ...
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2answers
63 views
Vacuum-ether and spacetime
in the past you could not give an explanation for various phenomena in
which was
an action at a distance like magnetism or gravity that occurred
in a vacuum;
For this reason, it was hypothesized ether ...
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2answers
200 views
Is the curvature of spacetime invariant? Could it be characterized as the ether?
I'm writing a paper for a Philosophy of Science course about GR/SR and I'm wondering if I can (1) characterize the curvature of spacetime as invariant and (2) argue that this is what Einstein referred ...
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1answer
176 views
Is the quantization of gravity necessary for a quantum theory of gravity? Part II
(At the suggestion of the user markovchain, I have decided to take a very large edit/addition to the original question, and ask it as a separate question altogether.)
Here it is:
I have since ...
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1answer
90 views
Relationship between a formal vector derivative and time evolution of an operator
I'm an undergraduate in physics, with all the lack of knowledge inherent in that. In two of my classes, my professors introduced two equations which look eerily similar. The first, from general ...
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1answer
136 views
Jacobi's matric formulation for tensors
Hi I am trying to derive the E field equation and am stuck using the Jacobi formula, is this correct: $$\delta \det g_{\mu \nu} = Tr(ADJ(g_{\mu\nu}\delta ...
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1answer
145 views
Hawking Radiation: how does a particle ever cross the event horizon?
The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation.
...
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1answer
117 views
Material strain from spacetime curvature
Let's say that you moved an object made of rigid materials into a place with extreme tidal forces. Materials have a modulus of elasticity and a yield strength. Does the corresponding 3D geometric ...
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1answer
91 views
Strings on a curved spacetime
Suppose we are interested in in string on a specific metric G, is it necessary to include a Dilaton field on back ground in order to preserve the Weyl invariance? suppose the spacetime is not empty, ...
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3answers
245 views
Similarity between the Coulomb force and Newton's gravitational force
Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
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4answers
342 views
Surely space-time Curvature does not explain gravity, it just describe its effects?
In special relativity co-moving objects see the other's 4-velocity as being only temporal.
When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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1answer
177 views
Scalar field stress energy tensor
Can anyone explain why $T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} $, other than justifying it from the einstein field equations?
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1answer
190 views
Boundary conditions of relativistic wave solutions?
If you take Einstein's field equations,
\begin{equation}
R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu},
\end{equation}
and you insert the metric
\begin{equation}
g_{\mu\nu} = \eta_{\mu\nu} ...
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1answer
51 views
Constraint on a metric
Given a metric of the form $$ds^2=dr^2+a^2\tanh^2(r/b)d\theta^2$$
why does it follow that $a=b$?
I can't quite spot a constraint condition...
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2answers
90 views
about the 1D singularity of black hole
I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the ...
2
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2answers
117 views
Does gravitational redshift imply gravitation time dilation?
The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
6
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2answers
161 views
Is the speed of sound almost as high as the speed of light in neutron stars?
Have you ever wondered about the elastic properties of neutron stars?
Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
2
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1answer
193 views
Covariant derivative
I would very much appreciate some help in The following:
What is 2nd order covariant derivative $$\nabla_i\nabla_jf(r)$$ in terms of $r,\theta, g(r)$ and partial derivative, given that the metric ...
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1answer
95 views
Flat space metrics
This question concerns the metric of a flat space:
$$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$?
Thanks.
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2answers
247 views
Question about proper time in general relativity
I think I may have some fundamental misunderstanding about what $dt, dx$ are in general relativity.
As I understand it, in special relativity, $ds^2=dt^2-dx^2$, we call this the length because it is ...
6
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0answers
139 views
Does local physics depend on global topology?
Motivating Example
In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology ...
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1answer
59 views
An infalling object in a black hole looks “paused” for a far away observer, for how long?
As I understand, to an observer well outside a black hole, anything going towards it will appear to slow down, and eventually come to a halt, never even touching the event horizon.
What happens if ...
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1answer
254 views
In what limit does string theory reproduce general relativity?
In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) ...
5
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0answers
86 views
Equation of state of cosmic strings and branes
I'm sure these are basic ideas covered in string cosmology or advanced GR, but I've done very little string theory, so I hope you will forgive some elementary questions. I'm just trying to fit some ...
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3answers
417 views
Why is $\langle \partial_{\mu} f(x) \rangle=0$?
I'm reading page 488 of Hobson, Efstathiou & Lasenby, and I don't understand something they write... so I came here.
The concept they describe is in linearised general relativity. In particular, ...
