All Questions
99
questions
2
votes
1
answer
109
views
Boundary conditions on transition maps on general relativity
On the initial courses of topology and differential geometry, we learn again and again about charts, and atlas, and transition maps. I feel that transition maps are a very powerful idea, because they ...
- 157
8
votes
1
answer
357
views
The synchronized clocks on earth's surface: at which observer's rate are they beating?
From what I understand, the time rates (I'm not speaking about absolute times) of all clocks on earth's surface are synchronized. This means that, say, a mobile phone's clock is generally not beating ...
- 3,753
3
votes
1
answer
90
views
Kruskal Diagram: 2D projection?
Is a Kruskal diagram a 2D flat space projection of Schwarzschild space-time diagram? If not, isn't it true that one could not draw one accurately on a paper?
BTW, I am not referring to Penrose ...
- 1,161
1
vote
0
answers
67
views
Chose coordinates where $g_{01}=g_{02}=g_{03}=0$ to disentangle space and time?
$g_{\mu\nu}$ is the metric tensor. It describes the curvature of spacetime in general relativity. The choice of coordinates is completely arbitrary. It should be possible to find and chose coordinates ...
- 93
2
votes
6
answers
2k
views
Is it possible to describe every possible spacetime in Cartesian coordinates? [duplicate]
Curvature of space-time (in General Relativity) is described using the metric tensor. The metric tensor, however, relies on the choice of coordinates, which is totally arbitrary.
See for example ...
- 93
3
votes
5
answers
535
views
Physical meaning of each component of the metric tensor in GR
I am searching, without success, what is the meaning of each component of the metric tensor in the context of General Relativity.
$$
g_{\mu\nu}=\left[\begin{matrix}g_{00}&g_{01}&g_{02}&g_{...
- 151
0
votes
0
answers
37
views
Diameter of a sphere in the regime of general relativity
Lets start naive: empty space, define the origin somewhere, start putting mirrors in a distance of $r$ in many directions so that they roughly sample the surface of a ball of radius $r$.
Someone ...
- 749
2
votes
2
answers
305
views
Derivation of the Schwarzschild metric: why are $g_{22}$ and $g_{33}$ the same as for flat spacetime?
I'm trying to understand the derivation of the Schwarzschild metric from Wikipedia, but I simply do not understand why, therein, $g_{22}$ and $g_{33}$ must be those of the flat spacetime.
Couldn't $g_{...
- 93
2
votes
1
answer
776
views
The value of speed of light in different regions of spacetime
This question of mine started shaping in my head first while I was looking for the most fundamental answer for the speed of light's value and its property of being the limit.
I have convinced myself ...
- 23
2
votes
1
answer
242
views
How to obtain orthonormal tetrad basis for an infalling observer?
An eternal Schwarzschild spacetime in Painlevé-Gullstrand coordinates reads as
$ds^2 = -\left(1-\dfrac{2m}{r}\right)c^2~dT^2 + 2\sqrt{\dfrac{2m}{r}}c~dTdr + dr^2 + r^2\left(d\theta^2+\sin{^2\theta}~d\...
- 756
22
votes
3
answers
3k
views
Why/When can we separate spacetime into space and time?
As far as I understand, for all practical applications in GR, we would need a way to split space and time. Since, often in practical applications and understanding physical phenomena, lengths and time ...
- 7,980
0
votes
1
answer
42
views
How is the time defined with paths consistent with the idea that we assign time to frames?
In 49:34 of this lecture by Frederic Schuller, it is explained that time is a derived quantity defined through this integral:
$$\tau = \int_{\lambda_o}^{\lambda_1} \sqrt{ g(v_{\gamma}, v_{\gamma}) }$$...
- 7,980
0
votes
2
answers
164
views
Observers in General Relativity: do transformations happen between two different observers or between two local coordinates both of the same observer?
In my understanding of general relativity, I am a little confused. Could someone please clarify this:
Given the definition of a manifold with its collection of subsets(patches) and mapping functions, ...
- 306
1
vote
2
answers
274
views
Proper time in a curved space
In special relativity we've the invariant
$$
d s^2=-d t^2 +d x^2 + d y^2+d z^2
$$
For a clock moving along the worldline in question the above equation reduces to $\begin{aligned} d s^2=&-d t^2\...
- 1,270
-8
votes
1
answer
158
views
Spacetime/spacetime interval in the light of this inquiry [closed]
As far as we know and the physics we have, Einstein's theory has been proven correct.
So we are left to say. That time and space as we intuively know them to be absolute and written in stone, they ...
- 107