Re: Symmetries of general relativity

Lubos Motl <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> On Sat, 1 Nov 2003, Fizz Fann wrote:
> 
> > Can you tell us how? Can you boost the Schwarzschild
> > solution for us?
> 
> Sure. I hope it's enough to tell you what you must do. Return to the
> coordinates x,y,z,t, for example by z=r.cos(theta),
> x=r.sin(theta).cos(phi), y=r.sin(theta).sin(phi) for the usual coordinates
> r,theta,phi,t of the Schwarzschild solution. Rewrite the solution in terms
> of x,y,z,t.
> 
> Then you substitute
>       x' = (t-v.x)gamma,      t' = (x-v.t)gamma
> 
> where v is some speed and gamma=1/sqrt(1-v^2). In terms of x',y,z,t' you
> will obtain a new solution of Einstein's equations that is related to the
> original one by a boost - you will obtain a boosted black hole. The fact
> that it is a solution is guaranteed by the symmetry of general relativity
> under any coordinate transformations.

Likewise, let's transform the Schwarzschild solution to rotating
oblate spheroid coordinates, and in this way derive the Kerr solution.
This should be ok, after all we wouldn't really want to suggest
that black holes can't rotate, right? :)