All Questions
13
questions
5
votes
2
answers
312
views
The limit of GR with infinite speed of light $c$
Just answer what you can. I don't mean the zero curvature flat space time version. I know that the Einstein Field equations use $c$ as a constant, but what would the universe be like if gravity was ...
- 83
2
votes
2
answers
461
views
Newtonian gravity as curvature of space
Since Newtonian gravity is also indistinguishable from acceleration, it should be possible to formulate it as a curvature in space, right? For example, if a body changes velocities purely under the ...
- 6,355
0
votes
6
answers
871
views
Can someone really explain the curvature of Spacetime?
I can understand the curvature of a sheet which is 2D but i can't understand the 3D curvature of space described in General Relativity. How's really the curvature of space described in GR? Could ...
user189508
0
votes
1
answer
75
views
Does intrinsic curvature in a higher dimension mean that the lower dimensions also exhibit curvature?
If our universe has intrinsic curvature in a higher dimension, would that mean the 3 dimensions that we live in would be curved? and if so would the lower dimensions exhibit intrinsic or extrinsic ...
- 23
1
vote
0
answers
120
views
Why do the ADM-energy, mass and linear momentum work?
In asymptotically flat spacetimes, the ADM-energy, linear momentum and mass are defined as
$$E:= \frac{1}{16\pi}\lim_{r\to\infty} \int_{S^2_r}\sum_{i,j}\partial_ig_{ij}-\partial_jg_{ii}\frac{x^j}{r}\...
- 113
1
vote
1
answer
426
views
How can existence of a timelike Killing field imply a metric that is independent of time coordinate?
I have read that the existence of an arbitrary timelike killing field implies that we can find some coordinates such that metric is independent of time in that coordinates. For me independence of ...
- 51
3
votes
0
answers
184
views
Doubt about energy conditions: the Time-like Convergence Condition
First of all, consider a congruence of smooth time-like geodesics parametrized by proper time $\tau$. So, a tangent vector to a time-like geodesic is indeed a four-velocity up to a factor constant; ...
- 3,085
2
votes
2
answers
209
views
Can I state that a spacetime is homogeneous and isotropic iff $\nabla_\mu R = 0$?
If a spacetime is homogenous and isotropic can I say that $\nabla_\mu R =0$?
I was reading this paper https://arxiv.org/abs/astro-ph/0610483 and, I think that is the justification for the authors ...
- 1,677
1
vote
1
answer
78
views
Gravitation function (or space-time distorsion variation) below Schwarzschild radius
Let's consider a massive sphere (with an approximate constant density, not charged, not rotating, no anti-matter for example an Earth simplified model).
On the outside of this sphere,
$g(r) = \alpha/{...
- 723
13
votes
1
answer
2k
views
What is the motivation from Physics for the Levi-Civita connection on GR?
On General Relativity the Levi Civita connection is quite important. Indeed, General Relativity is all about connecting the curvature of spacetime with the distribution of matter and energy, at least ...
- 36.4k
15
votes
1
answer
1k
views
How to measure Torsion and Non-metricity?
In General Relativity, we most often work with the Levi-Civita connection (metric and torsion-free). What kind of experiment can we make to be sure that our physical space-time indeed is torsion-free ...
- 199
161
votes
6
answers
55k
views
Why would spacetime curvature cause gravity?
It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" ...
- 1,926
9
votes
1
answer
694
views
Can masses move in 2+1 gravity?
I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
- 2,163