All Questions
14
questions
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
1
vote
1
answer
121
views
Does the spacetime curvature in the vicinity of a massive body increase, decrease or remain unchanged with the increasing velocity of an observer?
Does the spacetime curvature in the vicinity of a massive body such as the sun increase, decrease or remain unchanged with respect to an observer's increasing velocity relative to that massive body?
- 79
3
votes
4
answers
461
views
Why doesn't the curved spacetime curve the stick?
We know that gravity is not a force, but a curvature of the spacetime. This is a great visualization.
But I don't understand something. If we live on Earth in a curved spacetime, and this curvature is ...
- 161
0
votes
2
answers
150
views
If I can linearly map a metric onto the Minkowski metric, then is the original metric automatically flat?
Suppose I have a metric $g$ such that, via a linear coordinate transformation (i.e. a transformation represented by a non-singular matrix, not necessarily diagonal), I can rewrite $g$ as the Minkowski ...
- 103
1
vote
3
answers
430
views
Local inertial frames, and locally flat geometry, taylor expanding metric coefficients
In general relativity, if there is a line element of the form $$ds^2 = [f(u, v)]du^2 + [h(u, v)]dvdu + [w(u, v)]dv^2$$ which I believe corresponds to metric coefficients $$g_{00} = f(u, v)$$ $$g_{01} =...
- 11
1
vote
1
answer
149
views
Shape of curved spacetime?
Can the shape of curved space time under influence of mass be closely modelled by any function?
Like, without getting into tensors and Euclidean/non-euclidean geometry, can I make a function (in one ...
- 143
1
vote
1
answer
64
views
Some kind of slower time principle [duplicate]
I'm always trying to find underlying principles, like that the force is always directed toward a (locally) lower potential energy and alot of stuff like that.
Recently I've begun to gain some layman ...
- 165
2
votes
2
answers
266
views
Einstein equations in the spherically symmetric, static case
This question is not about the solutions but much rather about the equations we write in GR for a spherically symmetric, static vacuum 4D spacetime.
The Einstein equations are
$$G_{\mu\nu}=0\;\;\;\...
- 1,874
5
votes
2
answers
657
views
1+1D curved spacetime diagram example
This is a very basic question about General Relativity. I haven't take any GR course yet.
Suppose a flat spacetime with one space direction and one time direction, as follows:
Now add a mass at rest ...
- 1,872
2
votes
2
answers
819
views
Why does a flat metric imply coordinates?
When in a completely flat spacetime, a metric $\eta_{\mu\nu} $ implies that in a stationary reference frame, you are dealing with three cartesian space coordinates, and one time coordinate. On a ...
- 427
1
vote
2
answers
89
views
Is measurement of coordinates possible near strong gravity?
We know that Schwarzchild metric describes an asymptotically flat spacetime. This means that far away from the event horizon we can safely interpret the $r$ coordinate as distance from the center.
...
user56963
1
vote
1
answer
573
views
How is Riemann tensor related to the curvature in the coordinates?
I came across statements such as "the acceleration observed in a weak gravitational field is mainly due to curvature in the time coordinate. "
I want to know how we can explicitly find the curvature ...
- 372
4
votes
2
answers
822
views
Can a curvature in time (and not space) cause acceleration?
I realize that the curvature of space-time causes acceleration (gravity).
Is it possible to have a curvature only of space, or a curvature only of time?
If so, would a curvature only of space, or a ...
- 335
5
votes
3
answers
705
views
A thought experiment on vision and curved spacetime
What follows is a long self-made example to deal with my conceptual issues of visualizing curved spacetime.
Imagine an observer floating somewhere in space.
He feels no strain on his body, ...
- 1,379