- #1
darida
- 37
- 1
Ansatz metric of the four dimensional spacetime:
[itex]ds^2=a^2 g_{ab}dx^a dx^b - du^2[/itex]
where:
[itex]a,b=0,1,2[/itex]
[itex]a(u)=[/itex]warped factor
Christoffel symbol of a three dimensional AdS spacetime:
[itex]\Gamma^{c}_{ab}= \frac{1}{2} g^{cd}(∂_b g_{da} + ∂_a g_{bd} - ∂_d g_{ba})[/itex]
Now how to find [itex]\Gamma^{a}_{b}[/itex]?
[itex]ds^2=a^2 g_{ab}dx^a dx^b - du^2[/itex]
where:
[itex]a,b=0,1,2[/itex]
[itex]a(u)=[/itex]warped factor
Christoffel symbol of a three dimensional AdS spacetime:
[itex]\Gamma^{c}_{ab}= \frac{1}{2} g^{cd}(∂_b g_{da} + ∂_a g_{bd} - ∂_d g_{ba})[/itex]
Now how to find [itex]\Gamma^{a}_{b}[/itex]?