All Questions
4
questions
2
votes
1
answer
431
views
Contracting lightlike vector with timelike/spacelike vectors
Working in GR (3+1 dimensions) with a certain metric, I would like to understand what result I get contracting a lightlike four-vector with a spacelike and/or a timelike four-vectors (I'm interested ...
- 69
1
vote
1
answer
707
views
Finding the correct Christoffel-symbols in a 2+1D space-time
I'm trying to calculate the Christoffel Symbols in a 2+1D space-time with the following metric:
$$ds^2 = N^2(\vec r)c^2dt^2-\phi(\vec r)(dx^1)^2-\phi(\vec r)(dx^2)^2$$
To find the Christoffel ymbols ...
- 1,373
3
votes
2
answers
314
views
Restriction of a Lagrangian
I'm wondering if anyone could help me with the following questions.
Let $M$ be the Minkowski spacetime, given $f\in C^{\infty}(M) ; f(m)=x^{0}(m)$, with $\{x^{\mu}\}$ being a global Cartesian ...
- 313
1
vote
1
answer
220
views
Killing vector argument gone awry?
What has gone wrong with this argument?!
The original question
A space-time such that $$ds^2=-dt^2+t^2dx^2$$
has Killing vectors $(0,1),(-\exp(x),\frac{\exp(x)}{t}), (\exp(-x),\frac{\exp(-x)}{t})...
- 13