# Spacelike and Timelike singuralites

1. May 27, 2010

### off-diagonal

I've read about Schwarzschild and Kerr metric, I confused about the spacelike singularity(occur in non-rotating metric) and timelike singularity (Kerr, RN).

In Schwarzschild case, when we cross and event horizon $$r=2M$$ metric component switch sign between time and radial component of metric tensor. That cause to the unavoidable trip to the singularity at $$r=0$$ when cross the event horizon. But In the Kerr black hole, There is a timelike singularity which one can avoid to reach the "ring singularity" of Kerr metric.

My question is, What is Timelike and Spacelike singularity? What is the different between them?

How can I physically interpret the significant of sign switching of $$g_{tt}$$ when across the particular surface?

PS , for Schwarzschild this surface appears once at event horizon, however, for the Kerr metric the sign has changed twices, i.e. Infinite redshift surface $$S^{\pm}$$

2. May 27, 2010

### sheaf

You probably have to look at the definitions of spacetime singularities in terms of geodesic incompleteness. The singularity is where the geodesic is trying to go if you were able to extend it.

For the behaviour of the Schwarschild metric at the horizon, you may need to switch to Kruskal coordinates (google will turn lots of information up) to see what is or isn't happening there.

I think (hopefully some expert will correct this if I'm wrong!): in a geodesically incomplete (i.e. singular) spacetime, a spacelike singularity is where timelike geodesics would like to end up, and a timelike singularity is where spacelike geodesics would like to end up.

Last edited: May 27, 2010
3. May 28, 2010

### stevebd1

This might also shed some light on the difference-

http://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems" [Broken]

Last edited by a moderator: May 4, 2017