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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5answers
575 views
How does the string worldsheet affect the space-time in which they live?
I don't understand much about string theory and never really got much further past the Nambu-Goto action and very basic supersymmetry (SUSY) lectures in my undergraduate courses, but the only thing ...
2
votes
2answers
604 views
Are neutrinos affected by gravity?
Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons ...
10
votes
0answers
275 views
A dictionary of string - standard physics correspondences
Motivated by the (for me very useful) remark
''Standard model generations in string theory are the Euler number of
the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3
...
3
votes
0answers
401 views
Derivation of the Gauss-Codazzi equation
I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface.
$$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$
...
3
votes
2answers
177 views
Clarification on Wald's book
I have a question concerning the Wald's book: General Relativity.
In the appendix E, he derived the Einstein equation by considering the surface term (GHY).
I do not understand what he said after the ...
9
votes
1answer
180 views
What does the equivalence principle mean in quantum cases?
We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear.So is there any similar situation in the case of electron near the ...
1
vote
1answer
206 views
What is the fate of a 3-Torus universe?
Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?
0
votes
2answers
189 views
How can we model intrinsic curvature?
Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?
1
vote
1answer
164 views
Why is the universe described in terms of Euclidean space and not Minkowski spacetime?
The universe is described as an infinite Euclidean space in cosmology. Why isn't it treated as Minkowski spacetime?
1
vote
2answers
156 views
How to deal with the product of distributions by Renormalization or similar?
how can we deal for example with the product of distributions in physics ?? is there any mean to define with physics $ \delta ^{2}(x) $ or to treat a product of two distributions within the ...
4
votes
3answers
173 views
Twin paradox - observers counter orbiting Earth
Imagine three observers - one (A) stationary on the surface of Earth (latitude 0 deg) and two others orbiting the planet in the same circular equatorial orbit just in the opposite direction. When the ...
3
votes
1answer
133 views
Simulating a black hole binary system
As part of a project for my degree I am writing code to simulate N-body gravitational interactions, however I have to then use this code to investigate something. Struggling to think of ideas I ...
8
votes
4answers
325 views
What makes the stars that are farther from the nucleus of the galaxy go faster than those in the middle?
It has no sense that stars that have a bigger radius and apparently less angular speed($\omega$) goes faster than the ones near the center.
2
votes
2answers
709 views
Faster-than-light communication using Alcubierre warp drive metric around a single qubit?
The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
1
vote
2answers
520 views
How do we determine the temperature of a Black Hole?
How do we determine the temperature of a Black Hole?
Since we cannot see a Black Hole, which I presume, is because it absorbs light, would it not also prevent radiation from escaping, making ...
4
votes
1answer
625 views
Why is light described by a null geodesic?
I'm trying to wrap my head around how geodesics describe trajectories at the moment.
I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
1
vote
2answers
154 views
Computing the path of photons near a black hole
For a simulation, I want to compute the path that light follows near a black hole.
Non-relativistically, a massive point particle in a central newtonian gravitational field follows either an ellipse, ...
6
votes
1answer
282 views
Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?
The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
-1
votes
2answers
99 views
The relativistic mechanics of a battery that is being charged and accelerated at the same time
This might be an interesting question:
Let's attach a battery into one end of an electric cable. Then we rotate the battery around, with accelerating speed, using 100 Watts of power, while the ...
9
votes
2answers
598 views
Does a photon exert a gravitational pull?
I know a photon has zero rest mass, but it does have plenty of energy. Since energy and mass are equivalent does this mean that a photon (or more practically, a light beam) exerts a gravitational pull ...
0
votes
2answers
343 views
Abstract Algebra in Relativity and Cosmology?
Is Abstract Algebra useful in theoretical Relativity and/or Cosmology? If so can anyone give me some examples or point me towards a good book with that emphasis if it is one?
Thanks in advance.
9
votes
3answers
472 views
Why does large curvature of spacetime imply high temperature?
I`ve just stumbled about a sentence which says that high curvature of spacetime implies that any matter present is at high temperature.
This somehow confuses me, so my probably dumb question(s) are:
...
4
votes
2answers
186 views
Are we going to be able to travel trough space deforming the space-time?
I'm not talking about the speed of the spaceship. If we can deform space-time we needn't any type of propulsion. And how can the travel affect to it's pilots? Can they survive?
7
votes
2answers
163 views
Equivalence of definitions of ADM Mass
ADM Mass is a useful measure of a system. It is often defined (Wald 293)
$$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$
Where $s_r$ is two ...
5
votes
3answers
179 views
Tension on a cable in a gravitational field
Consider a mass 'm' suspended in the gravitational field of a massive star. Assuming the Schwarzschild metric it is easy to calculate the gravitational acceleration at the location of the mass and ...
4
votes
2answers
344 views
Does spacetime in general relativity contain holes?
Are there physical models of spacetimes, which have bounded (four dimensional) holes in them?
And do the Einstein equations give restrictions to such phenomena?
Here by holes I mean ...
1
vote
3answers
244 views
Evidence that “space exists rather than just particles”
What is (theoretical) evidence that you need to define all of space with properties rather than just stating where all particles are? I mean, does every single coordinate x, y, z have a meaning or ...
3
votes
2answers
351 views
Lorentz invariance of the 3 + 1 decomposition of spacetime
Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is ...
2
votes
1answer
132 views
Derivative of quantities with internal indices
In the context of the 3 + 1 decomposition of spacetime needed for a Hamiltionian formulation of general relativity, quantities with so called internal indices are introduced (in the book I am reading ...
2
votes
1answer
90 views
Question from Schutz's
In q. 22 in page 141, I am asked to show that if $U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta}$, then $U^{\alpha}\nabla_{\alpha}V_{\beta}=W_{\beta}$.
Here's what I have done:
$V_{\beta}=g_{\beta ...
1
vote
2answers
139 views
Finding the correct units for the energy-momentum tensor?
I'm trying to understand the energy-momentum tensor $T^{\mu\nu}$ but I'm confused about the units. My textbook says the components of $T^{\mu\nu}$ are $\mathrm{Jm^{-3}}$. Four-momentum is is given ...
2
votes
1answer
196 views
How do I calculate the induced metric in the Gibbons–Hawking–York boundary term?
This question concerns the expression for the induced metric in the explicit variation of the GHY boundary term. Just how is that expression derived in detail from the definition of the induced metric ...
5
votes
3answers
203 views
From the perspective of an observer inside a black hole's horizon, where does the energy for Hawking radiation come from?
Would energy be seen to "flow" to the outside of the black hole? Through what mechanism?
4
votes
1answer
108 views
Hawking radiation: direct matter -> energy conversion?
When a black hole evaporates, does it turn all the matter that has fallen in directly to energy, or will it somehow throw back out the same kind of matter (normal or anti) that went in?
11
votes
2answers
610 views
Does a charged particle accelerating in a gravitational field radiate?
A charged particle undergoing an acceleration radiates photons.
Let's consider a charge in a freely falling frame of reference.
In such a frame, the local gravitational field is necessarily zero, ...
5
votes
3answers
89 views
Analyticity and Causality in Relativity
A few weeks ago at a conference a speaker I was listening to made a comment to the effect that a function (let's say scalar) cannot be analytic because otherwise it would violate causality. He didn't ...
4
votes
2answers
333 views
Deriving Birkhoff's Theorem
I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
5
votes
2answers
210 views
What should be the equation satisfied by The Momentum commutators in a curved background?
This may be obvious but I have limited experience in physics , The generators of Spatial translation symmetry commutes with each other i.e [P(i),P(j)] = 0 but if Spacetime is a curved manifolds then ...
6
votes
2answers
310 views
Have red shifted photons lost energy and where did it go?
I think the title says it. Did expansion of the universe steal the energy somehow?
7
votes
2answers
271 views
Equivalence principle and radiation from falling particle
I am currently having a hard time solving a problem of GR from Lasenby's book.
I can't make it more clear than by quoting the exercise:
7.2 A charged object held stationary in a laboratory on the ...
3
votes
2answers
220 views
A simple thought experiment about traversable wormholes
Let's say I have a tube, of large radius (about 5 - 7 meters in diameter), with traversable wormholes at the ends. The wormholes are arranged as such that if something falls inside one hole from ...
3
votes
5answers
515 views
Can you use a wormhole to travel through space not time?
I want to know if you could theoretically travel from your house to work via a wormhole but stay in the present day...without changing time. Kind of like teleportation but harnessing the energy of a ...
2
votes
1answer
198 views
Experimental proof of gravitational redshift of light
Has the gravitational red shift been proven for electromagnetic waves only or also for a single photon?
15
votes
8answers
2k views
How can anything ever fall into a black hole as seen from an outside observer?
The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a ...
2
votes
1answer
343 views
Stokes' theorem in GR
I read this formula in Sean Carroll's book of GR:
$$\int_{\Sigma}\nabla_{\mu}V^{\mu}\sqrt{g}d^nx~=~\int_{\partial\Sigma}n_{\mu}V^{\mu}\sqrt{\gamma}d^{n-1}x$$
where n is the 4-vector orthogonal to ...
2
votes
1answer
294 views
Discrete point particles stress energy tensor
I am trying to solve an exercise in Sean Carroll's GR book "Spacetime and Geometry". Basically we need to derive the stress-energy tensor of a perfect fluid (ie $T^{\mu\nu}=(\rho +p)U^{\mu}U^{\nu} + ...
2
votes
2answers
120 views
How to test whether galaxies are moving away from each other in a static background or whether space is being created beween them?
Observations show that galaxies are moving away from one another on the macroscopic scale.
Now, scientists interpret this by saying this happens not because galaxies are really moving away from each ...
2
votes
1answer
157 views
Contraction of indices
We use contraction of indices method to manipulate Tensors. However, I cannot relate that manipulation visually. We can change covariant tensor to contravariant tensor and vice versa by contracting ...
5
votes
2answers
540 views
Visualizing Ricci Tensor
By definition Ricci Tensor is a Tensor formed by contracting two indices of Riemann Tensor. Riemann Tensor can be visualized in terms of a curve, a vector is moving and orientation of the initial and ...
7
votes
1answer
88 views
Fourier Methods in General Relativity
I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
