Penrose-Diagram for the Kerr-Metric

[Clausalism]

Hey Guys,

so i was reading Hawking&Ellis a bit and still encounter always problems with the Penrose-Diagrams. Looking at the Penrose-Diagram for the rotating Kerr-Black hole (just one illustrating picture at the end) i come up the following question:

There are two regions III (with the singularites inside) which are seperated from each other. Given i am in the region II (between the chauchy-surfaces, where only the r coordinate is well defined) how would you describe the trajectories of observers who want to go to either one of the two singularities? In other words how would you control your trajectory to do that (i.e., what measurements you would make to ensure that you ended up in, say, the "left" singulartiy-region III as opposed to the right one)?

Thank your very much for your answer!

[MigL]

Just noticed this, so here's my two cents.

 

Penrose diagrams are basically two dimensional light cones such that the 45 deg line is c .

Obviously speeds are constrained to be equal to or more vertical than 45 deg, and the horizon itself is at 45 deg since it denotes an escape velocity of c . In effect, atwo dimensional finite 'mapping' of an infinite space-time.

Even in a regular Swartzchild ( non-charged, non-rotating ) BH Penrose diagram, there are two horizons, whether this has any physicality is open for debate, but obviously cannot be verified and settled.

Similarily a Kerr BH ( or a Nordstrum BH ) Penrose diagram has more than one horizon and various other 'regions' which can be accessed by travelling slower than c , but again, they may not have any physical meaning such as different universes, different areas of the same universe, or absolutely nothing.

[Clausalism]

Thank you for your reply.

 

I agree with what you said completley: These regions may have no physical meaning, maybe not even exist at all. But now just take the picture you get from general relativity as it is and assume this maximal analytic extension would be correct. How would you - in this mathematical framework - be able to choose to which region III you travel?