- #1

Buzz Bloom

Gold Member

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https://www.physicsforums.com/threads/qs-re-hawking-radiation-part-i.873163/reply?quote=5482437

I asked if there were any errors in my summary description of the Hawking radiation phenomenon. So far none have been posted.

In this thread I want to learn some additional facts about the phenomenon. Can someone please tell me, in terms of the Schwartzchild metric, what the BH energy density is of the gravitational field at radius

r > R

_{c}.

I am guessing that this energy density is functionally related to the scalar curvature at r. I found the following formula for this scalar at

http://www.physicspages.com/2014/03/16/riemann-tensor-in-the-schwarzschild-metric/ .

I think that this form assumes c = 1. Therefore 2GM = R

_{c}, and the scalar can then be written as:

(R

_{c}/r

^{3}) × ( 1 - R

_{c}/r)

^{-1}

In SI units this scalar has the units m

^{-2}. Therefore, I assume that it is not the curvature, but the rather the curvature squared, and the actual curvature scalar is equal to the squareroot of this expression.

If my guess is correct, what is the functional relation between the curvature and the gravitational field energy density?