The "surface gravity" of a black hole is defined as the force required "at infinity" to hold an object at rest at the horizon. The Wikipedia page gives a brief discussion:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Surface_gravity

This has also been discussed on PF before, for example in this thread:

https://www.physicsforums.com/showthread.php?t=405941

I've also seen this subject treated in textbooks; I believe it's covered in Wald's GR textbook (I actually encountered it first in his book "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics"). I understand the basic derivation and why the "surface gravity" is finite even though the acceleration required "locally" to hover at rest diverges at the horizon.

My question is whether the idea of "holding an object at rest at the horizon", even if we measure the force required "at infinity" so it's finite, makes sense. The horizon is a null surface, so any object "at rest" there would have to travel on a null worldline. The idea of holding "at rest" an object like a light beam doesn't really make sense to me. Is this just an indication that the "surface gravity" of the black hole can't be directly measured physically? Or does it indicate that the concept itself doesn't really make sense? I'd be interested in PF members' opinions on this.

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# Black hole surface gravity question

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