All Questions
Tagged with spacetime metric-tensor
571
questions
22
votes
2
answers
8k
views
How do I derive the Lorentz contraction from the invariant interval?
While reviewing some basic special relativity, I stumbled upon this problem:
From the definition of the proper time:
$$c^2d\tau^2=c^2dt^2-dx^2$$
I was able to derive the time dilation formula by using ...
- 16.4k
3
votes
1
answer
1k
views
Index raising and lowering - how does it work?
In the context of four-dimensional spacetime, how does the metric turn a tangent vector into a gradient, and vice versa? By this I mean that I know the metric can be used to raise and lower indices:
$...
- 3,059
3
votes
1
answer
2k
views
The most general form of the metric for a homogeneous, isotropic and static space-time
What is the most general form of the metric for a homogeneous, isotropic and static space-time?
For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
- 95
1
vote
0
answers
114
views
When is spacetime homogenous and isotropic? [duplicate]
When is spacetime homogenous and isotropic?
For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric
$$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + f(x^\mu)...
- 11
12
votes
4
answers
3k
views
How do you tell if a metric is curved?
I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - $M$...
- 3,727
1
vote
2
answers
269
views
How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?
The metric tensor for Fock-Lorentz space-time,
$$
\mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
user8817
0
votes
2
answers
673
views
What is the link between the metric signature of spacetime and fundamental field equations?
The signature of Minkowski spacetime is 2, as is explained here: Metric signature explanation. The signature is related to the form the fundamental equations take, but I'm not totally clear on the ...
- 431
2
votes
2
answers
376
views
Why can certain functions be absorbed into the Schwarzschild metric, while others can't?
Another question about the Schwarzschild solution of General Relativity:
In the derivation (shown below) of the Schwarzschild metric from the vacuum Einstein Equation, at the step marked "HERE," we ...
- 1,048
16
votes
4
answers
6k
views
What is 'past null infinity'?
For example, in the sentence "there is no incoming radiation at past null infinity".
- 2,283
70
votes
2
answers
9k
views
Is spacetime flat inside a spherical shell?
In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
- 2,163
12
votes
1
answer
952
views
Causal and Global structure of Penrose Diagrams
What kind of global and causal structures does a Penrose diagram reveal?
How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure?
Also,
I ...
- 121
12
votes
2
answers
1k
views
How much choice did Einstein have in choosing his GR equations?
General relativity was summarised by Wheeler as "Spacetime tells matter how to move; Matter tells spacetime how to curve". I have a fairly good mental picture of how the first part works.
However, I ...
- 34.3k
8
votes
4
answers
5k
views
Why is time-order invariant in timelike interval?
Why do two observers measure the same order of events if we are inside the light cone?
(e.g. if $ds^2 > 0$ time-order is preserved according to the classical mechanics book I am reading, but it ...
- 253
37
votes
8
answers
5k
views
Interval preserving transformations are linear in special relativity
In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity:
Prove ...
- 3,732
1
vote
1
answer
244
views
Can spacetime be defined by the requirement that the physical laws are simple?
When I was student I was told that time is defined by the requirement that the physical laws are simple. For example, in classical mechanics time can be defined by the requirment that the velocity of ...
- 23