All Questions
Tagged with time metric-tensor
44
questions
3
votes
1
answer
125
views
What is the problem with two time dimensions? [duplicate]
I am reading a book "General relativity: The theoretical minimum" by Leonard Suskind.
In page 168-169, the author explains the reason why we don't consider the case with two time dimensions ...
- 311
0
votes
0
answers
43
views
Time direction ambiguity in stationary observer's 4-velocity
Working in the mostly + convention, for a timelike geodesic in Minkowski spacetime we have the requirement that (c=1):
$$u^\alpha u_\alpha=-1$$
and that it of course obeys the geodesic equation.
If we ...
- 49
3
votes
2
answers
298
views
Time in the negative mass Schwarzschild solution
I have read that for the Schwarzschild metric solution with $M<0$, something odd happens with the time coordinate. For the constants of motion, $dt/d\tau=e(1 - 2GM/r)^{-1}$ with $M<0$ and $e$ a ...
- 476
1
vote
0
answers
74
views
Why can't the metric have more than one timelike coordinate? [duplicate]
In one of his lectures, L Susskind stated that he cannot make sense of a metric with more than one timelike dimension. I also have trouble imagining it, but is there a good mathematical or physical ...
- 795
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
0
votes
1
answer
142
views
Physical meaning of a time dependent $g_{00}$
I have been studying Birkhoff's theorem and, separately, co-moving coordinates.
One of the final steps in Birkhoff's theorem (from Weinberg's GR pg. 337) is to redefine the time coordinate to absorb ...
- 57
26
votes
9
answers
5k
views
Time is the only dimension that has an arrow, and the only dimension which contributes an opposite sign to the metric. Is that just a coincidence?
Time is different from space in these two seemingly independent ways.
One of them is generally believed to have to do with special boundary conditions at the beginning of time.
But if you knew nothing ...
- 1,821
0
votes
1
answer
139
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How to get Lorentz metric from a given light cone structure?
Given a Lorentz metric it's usually easy to figure out how the the light cone structure looks like (e.g. by calculating the null geodesics).
But is there a straightforward way to determine the ...
1
vote
1
answer
69
views
Riemannian manifolds with absolute time
Sorry for my math lacks, I hope you'll be patient even if this question will probably not be clear.
Is possible for an universe to have a curved space and an absolute time?
Would this universe have ...
- 97
2
votes
1
answer
284
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Proper time in General Relativity and change of coordinates
Let $M$ be the spacetime manifold and let us consider a local coordinate system \begin{align}
\varphi_i:\,U_i&\subset M\to \varphi_i(U_i)\subset \mathbb R^n,
\end{align}
which associates $p\in ...
- 195
0
votes
2
answers
133
views
What does the $t$ coordinate represent in a general metric?
I am learning general relativity, I understand that the metric tensor has a coordinate $t$ corresponding to time. But I know also that time depends on gravity and so the time can change from point to ...
- 385
6
votes
0
answers
143
views
In the context of condensed matter physics, what does it mean for time to have two dimensions?
In an online article that describes condensed matter physics for laypersons, the author describes various so-called "designer materials" that have exotic properties, including one in which ...
- 179
2
votes
1
answer
388
views
Proper time of a timelike geodesic
In the contest of the newtonian limit in general relativity, if I consider a timelike geodesic that can represent the motion of a free falling particle under the influence of the gravitational force ...
- 23
7
votes
0
answers
187
views
Correct statement of Birkhoff's theorem (spherically symmetric does not imply static?)
If I understand correctly, the appropriate statement of Birkhoff's theorem in general relativity is that
The Schwarzschild metric is the unique spherically symmetric vacuum
solution.
(Or we might ...
- 684
1
vote
2
answers
199
views
How can spacetime change with time?
As far as I understand, spacetime fuses the 3 dimensions of space with the dimension of time into a single entity. If there's a big curvature, things will experience a change in how they experience ...
- 13