What is the proper equation for relativistic escape velocity?

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Offline jeffreyH

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I have been looking around online for any pointers but there seems to be hot debate around this subject. I could try looking through the book Numerical Relativity but thought I'd ask here first.
Fixation on the Einstein papers is a good definition of OCD.


Offline PmbPhy

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It's the same idea as it is in non-relativistic mechanics; set the speed so that the particle comes to rest at infinity. In practice this comes to setting the speed to distance far away from the source of the field. The time component of the momentum 1-form is the energy of the particle so that has to equal the rest energy at that distance. Think about the steps that you take in non-relativistic mechanics and apply it to general relativity keeping in mind that it's P0 that's the energy of the particle. Don't make the mistake that so many people do in thinking that the time component of a particle's 4-momentum is energy because that's only true in the absence of a gravitational field and therefore only in globally inertial frames of reference.