$SO(p,1)$ transformation on black p-branes

Question

I'm working on Blackfolds at the moment and I'm trying to boost-rotate( $SO(1,p)$ ) the p-brane $$ds^2=ds^2_{Sch}+\sum_{i=1}^p dz_i^2$$ Where $ds^2_{Sch}$ is the Schwarzschild metric in $N$ dimentions.

Can anyone help me with this ? let's say for the easiest case of $SO(2,1)$ ? Thanks.

This post imported from StackExchange Physics at 2015-04-19 11:41 (UTC), posted by SE-user Nikos

Comments

feel free to boost it.... just like the flat case.

This post imported from StackExchange Physics at 2015-04-19 11:41 (UTC), posted by SE-user Alice Akitsuki

Answer 1

I think what you want to do is to split away the $-f dt^2$ term from the Schwarzschild piece of the line element, and join it with the $p$-brane directions. Then apply the usual boost to the $(t,z^i)$ coordinates. Because this isn't Minkowski space (the $f$ factor in front of $dt^2$), this won't be a symmetry and will result in the same solution expressed in different coordinates.

This post imported from StackExchange Physics at 2015-04-19 11:41 (UTC), posted by SE-user Surgical Commander

Comments

and what about the rotations ? because in p=2 i will have and the rotations (symmetry) between the $z^i$ :)

This post imported from StackExchange Physics at 2015-04-19 11:41 (UTC), posted by SE-user Nikos