Outgoing Eddington-Finkelstein coordinates

[VantagePoint72]

I'm not sure what's going on in outgoing Eddington-Finkelstein coordinates for a Schwarzschild black hole. Future-directed timelike curves can be followed from inside the event horizon to outside it (page 185/186 of Sean Carroll's online GR notes: http://preposterousuniverse.com/grnotes/grnotes-seven.pdf ). How is that possible? Wouldn't that imply that massive particles could escape from inside a black hole's event horizon? Kruskal coordinates make it crystal clear that all future directed timelike worldlines inside the event horizon end in the singularity, so I really can't see what the outgoing E-F coordinates are illustrating.

 

[PeterDonis]

Future-directed timelike curves can be followed from inside the event horizon to outside it (page 185/186 of Sean Carroll's online GR notes: http://preposterousuniverse.com/grnotes/grnotes-seven.pdf ). How is that possible? Wouldn't that imply that massive particles could escape from inside a black hole's event horizon?

No, it means that outgoing E-F coordinates cover a different portion of the total spacetime than ingoing E-F coordinates do. See below.

Kruskal coordinates make it crystal clear that all future directed timelike worldlines inside the event horizon end in the singularity, so I really can't see what the outgoing E-F coordinates are illustrating.

They are illustrating that timelike worldlines can *emerge* from the white hole singularity, come out through the white hole horizon, and enter the exterior asymptotically flat region. Outgoing E-F coordinates cover Region IV and Region I of the full (maximally extended) spacetime, where the "regions" are labeled as shown in this diagram:

http://en.wikipedia.org/wiki/File:Kruksal_diagram.jpg

Ingoing E-F coordinates cover Regions I and II. So the horizons and singularities that are "visible" in the two E-F charts are *different*.

 

[VantagePoint72]

Got it, thanks!