All Questions
73
questions
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Does Mass Actually Displace Space-Time, or does Mass only Distort it?
1. Question
Given the plethora of space-time illustrations, there is a sense that space-time is actually being displaced by mass, (planets). But on its face, this doesn't really make sense because ...
- 93
0
votes
0
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72
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How to mathematically describe the process of spacetime curvature?
I guess as a result of the energy-momentum tensor $T_{\mu\nu}$ coupling to a flat Minkowski metric, $\eta_{\mu\nu}$, the flat metric can become that of a curved spacetime, $g_{\mu\nu}$. How can one ...
- 357
2
votes
2
answers
189
views
Can $\mathbb{R}^4$ be globally equipped with a non-trivial non-singular Ricci-flat metric?
I'm self-studying general relativity. I just learned the Schwarzschild metric, which is defined on $\mathbb{R}\times (E^3-O)$. So I got a natural question: does there exist a nontrivial solution (...
- 107
2
votes
6
answers
2k
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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
2
votes
1
answer
134
views
How do you relate $\Omega_{k}$, the curvature term in the FLRW metric, to the radius of curvature?
I have assumed, for reasons a bit too detailed to go into here, that if $\Omega_{k}$, the curvature term in the FLRW metric, is equal to 1, then the radius of curvature is equal to 13.8 billion light ...
- 371
2
votes
3
answers
220
views
What is Dirac's reasoning when showing the curvature vanishing implies we can choose rectilinear coordinates?
In section 12 of Dirac's book "General Theory of Relativity" he is justifying the name of the curvature tensor, which he has just defined as the difference between taking the covariant ...
- 43
2
votes
3
answers
871
views
Is the metric tensor an intrinsic property of spacetime or is it coordinate dependent?
From Wikipedia:
From the coordinate-independent point of view, a metric tensor field is defined to be a nondegenerate symmetric bilinear form on each tangent space that varies smoothly from point to ...
- 500
0
votes
1
answer
153
views
General Relativity via light cones curvature?
Is it possible to reformulate general relativity as curvature of objects' light cones instead of curvature of spacetime?
- 3
1
vote
5
answers
1k
views
Is space-time made of something?
General relativity introduced to us "space-time curvature", and also told us that space can be warped, deformed or curved when mass is acting upon it. Mass has atoms and particles inside but ...
user339151
4
votes
3
answers
779
views
Is space — as opposed to space-time — curved by a gravitating mass?
Or is the question in the title fundamentally wrong? We label each point in space-time with four coordinate values, one of which typically is suggestively called $t$ for time. This made me think that ...
- 749
18
votes
5
answers
2k
views
Where is the Lorentz signature enforced in general relativity?
I'm trying to understand general relativity. Where in the field equations is it enforced that the metric will take on the (+---) form in some basis at each point?
Some thoughts I've had:
It's baked ...
- 183
0
votes
2
answers
109
views
Could time be a secondary effect due to curvature of space?
In general relativity, four-dimensional spacetime is considered and curvature is calculated for spacetime, not only space alone.
However, looking deeper into the equations, many sources of symmetry ...
user336075
0
votes
2
answers
135
views
How do we figure out what is the right geometry of space?
In page-319 of Visual Differential Geometry, the following is written:
When we speak of a solution to Einstein's equation, we mean a geometry of space time (defined by it's metric) that satisfies the ...
- 7,980
9
votes
1
answer
932
views
How can an observer observe the metric of spacetime?
I don't mean how can we measure the metric in practice. I only mean in principle. Suppose you are an omnipresent being, no experimental limitations. What measurements do you need to measure the metric ...
- 519
0
votes
0
answers
46
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How to calculate the stress-energy-momentum tensor of a field that leads to finite volume with infinite extension? [duplicate]
Let's assume a theoretical spherically symmetric metric which leads to a finite volume with infinite extension.
The metric is characterized by
$$\mathrm{d}s^2=-B\,c^2 \mathrm{d}t^2+A\,\mathrm{d}r^2+r^...
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