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Black hole falling time for external observer

  1. Sep 17, 2011 #1
    It is well know that it takes pi*m time to go from rest at the surface of a Schwarzschild black to the singularity. How much time does an external observer at infinity experience then in that time? How do I show it?
     
  2. jcsd
  3. Sep 18, 2011 #2

    Bill_K

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    Hm, well in the first place you cannot "start from rest" from the Schwarzschild surface, since it is a null surface. Only an outward going null geodesic can be at rest there, and any timelike curve will cross it with a nonzero inward velocity.

    The external time has already gone to plus infinity when you reach the Schwarschild surface. The inside is a different coordinate patch, in which the radial coordinate r has become the timelike coordinate. So whatever "time" it takes to fall from the horizon to the singularity, there is no way to correspond it to external time.
     
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