- #1
JustinLevy
- 895
- 1
Consider the Schwarzschild black hole vacuum solution. Now let a test particle drop from "coordinate rest" at a finite r, and watch it fall in.
Is there a coordinate transformation in which we go to a rotating frame where the black hole is now a Kerr black hole and the test particle follows the appropriate trajectory for the Kerr black hole vacuum solution?
If yes, then aren't the solutions related by a diffeomorphism and therefore "physically" the same thing. If no, what prevents us from mapping one static vacuum solution onto another?
Is there a coordinate transformation in which we go to a rotating frame where the black hole is now a Kerr black hole and the test particle follows the appropriate trajectory for the Kerr black hole vacuum solution?
If yes, then aren't the solutions related by a diffeomorphism and therefore "physically" the same thing. If no, what prevents us from mapping one static vacuum solution onto another?