Outgoing Eddington-Finkelstein coordinates

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In summary, outgoing Eddington-Finkelstein coordinates for a Schwarzschild black hole show that future-directed timelike curves can emerge from the white hole singularity and exit the black hole's event horizon, entering the exterior asymptotically flat region. This is possible because outgoing E-F coordinates cover a different portion of the total spacetime than ingoing E-F coordinates. Kruskal coordinates also illustrate this, with all future-directed timelike worldlines inside the event horizon ending in the singularity.
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VantagePoint72
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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 [Broken]). 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.
 
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LastOneStanding said:
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 [Broken]). 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.

LastOneStanding said:
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*.
 
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Got it, thanks!
 

What are Outgoing Eddington-Finkelstein coordinates?

Outgoing Eddington-Finkelstein coordinates are a type of coordinate system used in general relativity to describe the curvature of spacetime around a massive object, such as a black hole. They are based on the Eddington-Finkelstein coordinates, which were developed by British physicist Arthur Eddington and German physicist Martin Finkelstein in the 1920s.

Why are Outgoing Eddington-Finkelstein coordinates important?

Outgoing Eddington-Finkelstein coordinates are important because they allow us to better understand and describe the behavior of spacetime near massive objects, such as black holes. They are also useful for making predictions and calculations in general relativity.

How do Outgoing Eddington-Finkelstein coordinates differ from other coordinate systems?

Outgoing Eddington-Finkelstein coordinates differ from other coordinate systems, such as Schwarzschild coordinates, in that they are specifically designed to describe the outgoing motion of particles in a curved spacetime. This makes them particularly useful for studying the behavior of light and other particles near black holes.

What are some applications of Outgoing Eddington-Finkelstein coordinates?

Outgoing Eddington-Finkelstein coordinates have a variety of applications in astrophysics and cosmology. They have been used to study the behavior of light near black holes, the formation of accretion disks, and the evolution of gravitational waves. They have also been used to test the predictions of general relativity and other theories of gravity.

Are there any limitations to using Outgoing Eddington-Finkelstein coordinates?

As with any coordinate system, there are limitations to using Outgoing Eddington-Finkelstein coordinates. They may not be suitable for describing the behavior of particles that are not moving outward, and they may also break down at the event horizon of a black hole. Additionally, they may be difficult to visualize and understand, which can make them challenging to use for some researchers.

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