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.

learn more… | top users | synonyms (1)

1
vote
0answers
314 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 ...
6
votes
1answer
2k 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 ...
5
votes
1answer
165 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
70 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
83 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
230 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' ...
5
votes
1answer
235 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
166 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 ...
4
votes
3answers
578 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
54 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 ...
2
votes
2answers
610 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
417 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 $R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.
5
votes
3answers
349 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
59 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
200 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 ...
3
votes
1answer
294 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
269 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 ...
10
votes
4answers
1k 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, ...
3
votes
1answer
140 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?
8
votes
2answers
192 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 ...
4
votes
2answers
888 views

Graviton and photons interaction

If one believes in the theory of gravitons then by viewing a black hole you see gravitons affect photons. This in turn leads to the conclusion that force carrier's mass equivalences allow them to be ...
5
votes
1answer
112 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: ...
10
votes
3answers
1k 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 ...
9
votes
1answer
477 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 ...
20
votes
3answers
7k 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 ...
10
votes
3answers
642 views

Since there are gravitational lenses, are there gravitational mirrors?

Gravitational lensing is an observed phenomenon. Can one have a gravitational mirror? A slightly unrelated question: Can gravitational waves be reflected?
2
votes
2answers
10k 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 ...
6
votes
1answer
2k 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 ...
1
vote
4answers
5k 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, ...
3
votes
0answers
260 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
79 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 ...
1
vote
3answers
446 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
132 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
1answer
341 views

Homogeneous gravitational field and the geodesic deviation

In General Relativity (GR), we have the geodesic deviation equation (GDE) ...
-3
votes
2answers
1k 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?
2
votes
1answer
164 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 ...
3
votes
1answer
639 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
400 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
231 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 ...
3
votes
1answer
594 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: ...
2
votes
0answers
108 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
180 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
529 views

What is 'past null infinity'?

For example, in the sentence "there is no incoming radiation at past null infinity".
3
votes
1answer
435 views

How does one write the Einstein field equations in terms of Ricci tensor?

How can I go from the 'standard' Einstein equations $R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu}$ to these equations: $R_{\mu\nu} = \frac{8\pi G}{c^4}(T_{\mu\nu} - ...
10
votes
2answers
356 views

Stellar winds from neutron stars

It seems that this question has not really been explored in the literature. Do isolated neutron stars (which do not accrete material) emit stellar wind? If yes, what composition would it have? If yes, ...
4
votes
2answers
335 views

How does the evaporation of a black hole look for a distant observer?

Let's assume an observer looking at a distant black hole that is created by collapsing star. In observer frame of reference time near black hole horizon asymptotically slows down and he never see ...
6
votes
2answers
449 views

What is the “foamy space” hypothesis that has been debunked recently?

In "Space-Time Is Smooth, Not Foamy", a Space.com article, it is stated: In his general theory of relativity, Einstein described space-time as fundamentally smooth, warping only under the strain ...
1
vote
2answers
500 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
6
votes
1answer
331 views

Does conformal gravity explain the Bullet cluster lensing effects?

Conformal gravity is an "alternative" theory of gravity, where instead of using the Einstein-Hilbert action composed of the Ricci scalar, the square of the conformal Weyl tensor is used. It was ...
4
votes
3answers
386 views

Question on inflation

I have two particular questions regarding the inflationary scenario. They are: 1.) What is the physical origin of the inflaton field? 2.) Why has the potential of the inflation field its particular ...