The Kerr-Newman solution is a vacuum solution. First consider Schwarzschild solution - modified to have dark matter in the interior. By dark matter I mean an effective negative AdS cosmological parameter /\ < 0 coming from a virtual particle plasma in which the density of virtual fermion closed loops is greater than the density of virtual bosons.
The effective metric inside 2M is then (G = c =1)
g00 = 1 + 2VNewton = 1 - /\r^2
r < 2M
acceleration of static LNIF
g = - g00^-1/2d(VNewton)/dr = (1 - /\r^2)^-1/2/\r/2 attractive for AdS /\ < 0
i.e. g(r < 2M) = -(1 + |/\|r^2)^-1/2|/\|r/2
outside the horizon
g00 = 1 - 2M/r
r > 2M
g(r >2M) = -M/r^2(1 - 2M/r)^1/2
continuity at the horizon demands matching g
this is not possible because we have an exterior coordinate singularity with no interior coordinate singularity.
Suppose we use a cutoff at Planck length Lp - at the horizon
assume Lp << M to first order in Lp/M Taylor series
(1 - 2M/(2M + Lp)^-1/2 ~ (2M/Lp)^1/2 >> 1
|/\|2M(1 + |/\|4M^2)^-1/2 ~ (1/M)(M/Lp)^1/2
4M^2|/\|^2(1 + |/\|4M^2)-1 ~ 1/MLp
4M^2|/\|^2 ~ (1/MLp)(1 + 4M^2 |/\|)
We end up with a quadratic equation with 2 roots for |/\| in terms of the mass M and the Planck quantum gravity scale Lp. Here M means GM/c^2
4M^2|/\|^2 - (4M/Lp)|/\| - (1/MLp) ~ 0
the dimension of each term here is 1/Area
Is there a real root - and is the whole thing stable or not? - in Ray Chiao's sense
Before going further the above algebra needs to be checked for errors.
Begin forwarded message:
Date: December 17, 2010 1:44:38 PM PST
To: Raymond Chiao
Subject: Re: From Ray Chiao - UC Merced - instability of black hole horizon?
yes as a matter of principle your argument is correct - but it's similar to Poincare recurrence cycles - practically speaking it won't matter for astrophysics/cosmology - where it does matter is for Bohmian hidden variable models of quarks, leptons, & hadronic resonances as tiny Kerr-Newman black holes - but then you can have T = 0 (zero surface gravity) as I recall in the Kerr-Newman metric. But that may not be stable and that would suggest such a model for the electron for example could not work.
On Dec 17, 2010, at 1:31 PM, Raymond Chiao wrote:
But we are dealing here with matters of principle, not "practically speaking" or FAPP! --Ray
Oh, OK now that I have read Ray's paper. Yes, technically that's correct, but practically speaking the lifetime of a black hole scales as M^3 very long for astrophysical black holes. :-)
E.g. if Sun were a black hole it would take 10^67 years >>> effective lifetime of matter in the accelerating universe.
On Dec 17, 2010, at 12:58 PM, JACK SARFATTI wrote:
Begin forwarded message:
From: Raymond Chiao
Date: December 17, 2010 12:22:15 PM PST
Subject: Re: Ted Jacobson's hologram derives from Einstein's original LOCAL EEP (Dr. Quantum) v3
Hi Jack, I think that the thermodynamic equilibrium between a black hole and a heat bath at the same temperature (i.e., at the Hawking temperature) is unstable. See the attached memo addressed to the gravity seminar at UC Merced. I find this conclusion very disturbing.