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Tagged with relative-motion differential-geometry
4
questions
1
vote
1
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75
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Principle of Relativity and the invariance of Newton's law in IRFs
Newton's law are form invariant under the coordinate substitutions:
$$
\tilde{x^{i}}=x^{i}+a^{i}
$$
This means that Newtons' equation of motion,
$$
F^{i}=m \frac{d^{2} x^{i}}{d t^{2}}
$$
(where $i=1,2,...
- 11
5
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0
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173
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Sum of geodesic deviation around a triangle in curved spacetime?
So I was pondering about geodesic deviations and I'm confused about the following. Let's say I have $3$ geodesics $\gamma_1(t)$ , $\gamma_2(t)$ and $\gamma_3(t)$. I introduce a parameter $s$ such that ...
- 1,389
1
vote
1
answer
142
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Relative velocity and proper time derivative of geodesic deviation?
From wiki
To quantify geodesic deviation, one begins by setting up a family of closely spaced geodesics indexed by a continuous variable s and parametrized by an affine parameter $\tau$. That is, for ...
- 1,389
7
votes
1
answer
419
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How to calculate relative velocity in curved spacetime?
Is there a nice geometric way to calculate relative velocity in curved space time? I'm looking from something similar to how the separation vector $n$ between $2$ neighboring geodesics obey:
$$ \...
- 1,389