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.
5
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0answers
87 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 ...
2
votes
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, ...
4
votes
2answers
174 views
Does Kaluza-Klein Theory Require an Additional Scalar Field?
I've seen the Kaluza-Klein metric presented in two different ways., cf. Refs. 1 and 2.
In one, there is a constant as well as an additional scalar field introduced:
$$\tilde{g}_{AB}=\begin{pmatrix}
...
0
votes
3answers
102 views
Black hole accretion of dark energy
Dark energy physically can be interpreted as either a fluid with positive mass but pressure the negative of its density (pressure has units of energy/volume, and energy is mass), or a property of ...
1
vote
1answer
190 views
In what way is the Riemann curvature tensor related to 'radius of curvature'?
In Misner, Thorne & Wheeler, they say, in their delightful 'word equations' that
$$\left(\frac{\mathrm{radius\,\, of \,\,curvature}}{\mathrm{of\,\, spacetime}}\right) = ...
1
vote
1answer
103 views
What does it mean that Einstein's equations are hyperbolic-elliptical?
I says on Wolfram MathWorld that Einstein's field equations are a set of "16 coupled hyperbolic-elliptic nonlinear partial differential equations".
What does it mean that the equations are ...
1
vote
0answers
77 views
Divergence theorem over entire space on non euclidean spaces
I'm a physics major so bear with me here on the math. This is related to a problem from the textbook General Relativity - Wald. In classical electromagnetism if we have a vector field say $V$ defined ...
4
votes
4answers
314 views
Can a photon get emitted without a receiver?
It is generally agreed upon that electromagnetic waves from an emitter does not have to connect to a receiver, but how can we be sure this is a fact? The problem is that we can never observe non ...
1
vote
1answer
139 views
Do residents of the Hudson Bay area have more time?
Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world.
Does that mean that things in the Hudson Bay ...
4
votes
1answer
102 views
How is the direction of time determined in general relativity?
In special relativity every frame has its own unique time axis, represented in Minkowski diagrams by a fan-out of time vectors that grows infinitely dense as you approach the surface of the light cone ...
0
votes
1answer
58 views
Why must the gravitational wave components be much less than unity?
We start with the metric tensor
\begin{equation}
g_{\mu\nu}(x) = \eta_{\mu\nu} + h_{\mu\nu}(x)
\end{equation}
in the linearised theory, or
\begin{equation}
g_{\mu\nu}(x) = \bar{g}_{\mu\nu}(x) + ...
0
votes
0answers
58 views
Is there a book that discusses General Relativity in terms of Modern Differential Geometry? [duplicate]
All of the physics books that I've seen which discuss General Relativity do so in terms of coordinates - the tensor calculus - even though the naturally relevant entities are invariant under general ...
1
vote
2answers
77 views
Hamiltonian constraint in spherical Friedmann cosmology
I'm taking a GR course, in which the instructor discussed the 'Hamiltonian constraint' of spherical Friedmann cosmology action. I'm not quite clear about the definition of 'Hamiltonian constraint' ...
4
votes
1answer
121 views
Kaluza-Klein Christoffel Symbols
I have a question regarding the connection coefficients as they pertain to the following paper: http://www.weylmann.com/kaluza.pdf . When I try to calculate the 4D Christoffel symbols from the 4D part ...
6
votes
1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
3
votes
3answers
308 views
Why do clocks measure arc-length?
Apologies in advance for the long question.
My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
0
votes
0answers
27 views
Why does the local inertial compass coincide with the stellar compass?
I found this physics paper via a non-duality site and I wished that I could understand it. Could someone please either read it and explain it to me or else point me to pages that would help me ...
1
vote
2answers
142 views
Expression for distance of closest approach in Schwarzschild Geodesics
The Wikipedia article Two-body problem in General Relativity uses two length-scale variables, $a$ and $b$, to simplify the math. For some information about these, consider these statements from the ...
1
vote
2answers
159 views
What is the Riemann curvature tensor contracted with the metric tensor?
Can the Ricci curvature tensor be obtained by a 'double contraction' of the Riemann curvature tensor? For example
$R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.
4
votes
3answers
158 views
Setting up a local-coordinate system in space-time using only a single clock and light beams
I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please ...
1
vote
0answers
41 views
The definition of $f_{NL}$ and transfer function
To me there seems to be quite a few different definitions of $f_{NL}$ in cosmology and I would like to know if or how they are equivalent. Let me cite at least 3 such,
One can see the equation 6.71 ...
5
votes
2answers
184 views
Order = Energy = Mass?
Here is a following problem I encountered when chatting about physics with my friend:
Let us imagine a classical example of ordered state of matter in thermodynamic sense: let's take a cylinder ...
2
votes
1answer
89 views
Propagating degrees of freedom of graviton
What is the best way to see that the number of propagating degrees of freedom or gravitons in 3 dimensions is $0$ ? By graviton I mean the metric and NOT some topologically massive graviton that one ...
2
votes
4answers
160 views
Equivalence principle question
I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell ...
4
votes
3answers
231 views
Can spacetime exist in the absence of matter and energy?
I'm pretty sure Ernst Mach would have said that spacetime cannot exist without matter in it.
But I'm also pretty sure that a black hole can be described as a self-sustaining gravitational field, ...
2
votes
2answers
104 views
Does spacetime have momentum?
In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
9
votes
1answer
124 views
Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?
It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of ...
5
votes
1answer
75 views
Help with the understanding of boundary conditions on $AdS_3$
So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form:
...
6
votes
3answers
281 views
What is the capture cross-section of a black hole region for ultra-relativistic particles?
What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is
$$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$
for a Schwarzschild BH in the geometric ...
7
votes
1answer
230 views
How to thoroughly distinguish a coordinate singularity and a physical singularity
In a course on general relativity I am following at the moment, it was shown that the singularity $r=2M$ in the Schwarzschild solution is a consequence of the choice of coordinates. Introducing ...
4
votes
3answers
359 views
How does faster than light travel violate causality?
Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon ...
5
votes
2answers
183 views
Since there are gravitational lenses, are there gravitational mirrors?
Gravitational lensing is a physical observed effect. Can one have gravitational mirror?
A slightly unrelated question: Can gravitational waves be reflected?
0
votes
2answers
462 views
Newtonian gravity vs. general relativity: exactly how wrong is Newton?
Is there a simple function I can use to describe the difference between simple Newtonian dynamics and the actual observed motion? Or maybe some ratios for common examples of, say, the motion of stars ...
4
votes
1answer
366 views
Physical significance of Killing vector field along geodesic
Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter.
What physical significance do the scalar quantity ...
0
votes
4answers
201 views
The bigger the mass, the more time slows down. Why is this?
If I were to stand by a pyramid, which weighs about 20 million tons, I would slow down by a trillion million million million of second. Don't know if that's exactly right, but you get the point. Also, ...
0
votes
0answers
116 views
Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?
A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
3
votes
0answers
56 views
Gravitational effects and metric spaces
Could somebody please explain something regarding the Nordstrom metric?
In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies.
My ...
0
votes
3answers
127 views
where the proper time is invariant why $d\tau$ is not zero?
where the proper time is invariant why change (differential) in proper time $d\tau$ is not zero?
$\Delta \tau=\tau_f-\tau_i$
as i know.
$d(invariant)=0$
note to comment:
action
$S=-m_oc^2\int_C d\tau$
...
0
votes
1answer
77 views
Can the zeroth-component of a 4-velocity be negative?
Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks.
This is referring to $V^0$ for a curved space ...
0
votes
0answers
31 views
time oscillation
Can there be a situation, where the time dilation is oscillating, in the sense that one observer notes that the time for the other frame is moving faster then slower, etc...? Can this oscillation be ...
0
votes
1answer
115 views
Homogeneous gravitational field and the geodesic deviation
In General Relativity (GR), we have the geodesic deviation equation (GDE)
...
-4
votes
3answers
176 views
How can mass affect spacetime?
In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?
1
vote
0answers
78 views
Massless Dirac equation is Weyl covariant
Does somebody know how to show that the following equation is Weyl invariant?
$$\gamma^ae_a^\mu D_\mu \Psi=0$$
where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
2
votes
1answer
176 views
Difference between $\partial$ and $\nabla$ in general relativity
I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones.
In our lectures we just had $\partial_\mu$ which would have the plain partial ...
6
votes
1answer
273 views
Diffeomorphisms and boundary conditions
I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper.
I found this ...
2
votes
2answers
123 views
Curved space or curved spacetime?
As I understand it, you can have time + flat space = curved spacetime.
So, when one is trying to emphasise that there is a curvature to the space, is it more technically correct to say curved space ...
1
vote
1answer
200 views
Dirac Equation in General Relativity
Dirac equation for the massless fermions in curved spase time is $γ^ae^μ_aD_μΨ=0$, where $e^μ_a$ are the tetrads. I have to show that Dirac spinors obey the following equation:
...
1
vote
0answers
72 views
Showing that the Ricci scalar equals a product of commutators
I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
0
votes
1answer
99 views
How would it be to look at the sky if the earth were near the edge of the universe?
By looking at this picture:
http://earthspacecircle.blogspot.com/2013/01/earths-location-in-universe.html
The earth is near the center of the universe. I've read that the universe look the same no ...
1
vote
2answers
99 views
What is 'past null infinity'?
For example, in the sentence "there is no incoming radiation at past null infinity".
