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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

g(r > 2M)  ~ - (1 - 2M/(2M + Lp)^-1/2 2M/(2M + Lp)^2

assume Lp << M to first order in Lp/M Taylor series

(1 - 2M/(2M + Lp)^-1/2 ~ (2M/Lp)^1/2  >> 1

matching g

|/\|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:

From: JACK SARFATTI <sarfatti@pacbell.net>
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

On Fri, Dec 17, 2010 at 1:24 PM, JACK SARFATTI <sarfatti@pacbell.net> wrote:
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
To: JACK SARFATTI <sarfatti@pacbell.net>
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.
 
--Ray Chiao



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