Spacelike and Timelike singuralites

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In summary, we discussed the Schwarzschild and Kerr metrics and the concept of spacelike and timelike singularities. We learned that in the Schwarzschild case, crossing the event horizon leads to an unavoidable trip to the singularity at r=0 due to a switch in the sign of the metric component between time and radial components. In the Kerr black hole, there is a timelike singularity which can be avoided, known as the "ring singularity" of the Kerr metric. We also explored the physical interpretation of the sign switching of g_{tt} and the existence of an infinite redshift surface in the Kerr metric. Finally, we discussed the definitions of spacetime singularities in terms of geodesic incom
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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 [tex]r=2M[/tex] metric component switch sign between time and radial component of metric tensor. That cause to the unavoidable trip to the singularity at [tex]r=0[/tex] 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 [tex]g_{tt}[/tex] 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 [tex]S^{\pm}[/tex]
 
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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 Schwarzschild 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.
 
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This might also shed some light on the difference-

http://en.wikipedia.org/wiki/Penrose%E2%80%93Hawking_singularity_theorems" [Broken]
 
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1. What are spacelike and timelike singularities?

Spacelike and timelike singularities are two types of singularities that can occur in space-time. Singularities are points in space-time where the curvature becomes infinite, and the laws of physics no longer apply. Spacelike singularities are points where space becomes infinitely curved, and timelike singularities are points where time becomes infinitely curved.

2. How are spacelike and timelike singularities different?

The main difference between spacelike and timelike singularities is the direction of the infinite curvature. In spacelike singularities, the infinite curvature occurs in space, while in timelike singularities, the infinite curvature occurs in time. This means that the laws of physics would break down in different ways at these two types of singularities.

3. What is an example of a spacelike singularity?

An example of a spacelike singularity is the singularity at the center of a black hole. At the center of a black hole, the gravitational pull becomes infinitely strong, and the laws of physics as we know them break down. This is because the space around the singularity becomes infinitely curved, creating a spacelike singularity.

4. How are spacelike and timelike singularities related to the Big Bang?

The Big Bang is thought to have been a timelike singularity, where time itself began and the laws of physics did not apply. This singularity is different from a spacelike singularity in that it is not associated with a point in space, but rather a point in time. The Big Bang is the starting point of our universe's expansion, and it is still not fully understood by scientists.

5. Can spacelike and timelike singularities be observed?

Currently, it is not possible to observe spacelike and timelike singularities directly. These points in space-time are hidden behind event horizons, making them impossible to see. However, scientists can study the effects of these singularities on the surrounding space and make predictions about their behavior using mathematical models and theories, such as general relativity.

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