What is the total mass of the accelerated viewpoint particle atmosphere of a black hole?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.443, just above Figure 12.5:

Surprisingly, from the accelerated viewpoint, the vacuum fluctuations consist not of virtual particles flashing in and out of existence, but rather of real particles with positive energies and long lives...

All of us in the at-rest universe outside the black hole are part of the accelerated viewpoint, since any one of us could in principle drop a line down to suspend a local observer near the hole surface, and from that accelerated viewpoint observe the quite real atmosphere of the hole.

Given the mass of the black hole, what is the equation for the finding the ratio (call it $A_m$ for now) of the total mass of this real-particle atmosphere to the total mass of the black hole?

• I think it's time-dependent, since some of those particles escape as Hawking radiation, so more and more of the mass will become "atmosphere" as the hole evaporates. – Nathaniel Nov 29 '13 at 1:18