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We compute the total power P by multiplying the far-away redshifted energy density by the area A of the horizon. This may be a conceptual error in Hawking's original estimate of black hole evaporation time. The clock hovering at L distant from A is running much faster than our far away clock where we are. A is an infinite redshift surface, but including L makes it finite but large. Also it takes infinite far away clock time for objects to reach A etc.
Therefore, we can argue that the Wikipedia calculation is wrong. That is, for Hawking's surface gravity case, replace
P ~ A (energy density) ~ A^-1
P ~ g00(L)^1/2A (energy density)
~  [1 + z(L)]^-1A (energy density)
~ (L/A^1/2)^1/2A^-1
Therefore, even in Hawking's case, 
P ~ dM/dt ~ L^1/2/A^5/4
dM/dt ~ L^1/2/M^5/2
tHawking ~ M^7/2 /L^1/2  not M^3
remember there is no actual evidence for M^3.
Next our new case
Instead of
P' ~ AT'^4 ~ A/L^2A ~ L^-2 ~ mp^-2
dM'/dt ~ mp^-2
P' ~ [1 + z(L)]^-1AT'^4
~ (L^1/2/A^1/4)A/L^2A
~ 1/L^1/2A^1/4
dM'/dt ~ 1/L^1/2M^1/2
t' ~ L^1/2M^3/2

to be continued

Putting in some numbers
From Wiki
Stefan–Boltzmann–Schwarzschild–Hawking black hole radiation power law derivation:
For a solar mass black hole
Putting in the gravity time dilation factor L^1/2/A^1/4
L ~ 10^-35 meters
L^1/2 ~ (1/3) 10^-17
A^1/2 ~ 10^3 meters

A^1/4 ~ 3 x10
L^1/2/A^1/4 ~ 10^-17/3x3s10 ~ 10^-19
P ~ 10^-28 x 10^-19 ~ 10^-47 watts
Next for our gravity radiation
P' ~ [1 + z(L)]^-1AT'^4 ~ (L^1/2/A^1/4)A/L^2A ~ 1/L^1/2A^1/4

P' ~ 6 x 10^-8T'^4
Our T' = (A^1/2/L)^1/2T ~  10^23(M/mp)^1/2(1/M) ~ 10^23/(mpM)^1/2  deg K
Therefore, energy density is
6 x 10^-8 x 10^92/mp^2M^2
Multiply by the area A and the gravity time dilation factor L^1/2/A^1/4
So that's effective area    L^1/2A^3/4
Total power is then
P' ~ 10^85 L^1/2A^3/4/mp^2M^2  Watts
for a solar mass scale black hole that's roughly
P' ~ 10^85 (1/3) 10^-17 (10^6^)3/4 10^10 x 10^-60  Watts
P' ~ 10^23 Watts - very roughly in gravity wave black body radiation ~ 
peak wavelength ~ 10^-16 meters ~ 10^24 Hz
to be continued - next order of biz evaporation lifetime

The 10^23 Watts is only the initial output - that increases as the black hole evaporates

Putting in some numbers
From Wiki
In our new theory this is I think
t'ev = c^2(mpM)^3/2 /3Kev 
(mpM)^3/2 = xM^3
x = (mpM)^3/2/M = (mp/M)^3/2
t'ev = (mp/M)^3/2 tev ~  (mp/M)^3/2 10^-16[M/kg]^3
For a ~ solar mass black hole 
(10^ -35)3/2 10^67 years ~ 10^-52 10^67 ~ 10^15 years

On Dec 5, 2013, at 7:55 PM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

From the beginning:
First Hawking
L = Schwarzschild radial coordinate distance to horizon classical 2D surface g00 = 0.
Newton's surface gravity ~ A^-1/2
A = area-entropy of g00 = 0
What they do in Wikipedia above comes down to this
Redshifted Unruh temperature a long distant from the black hole is
THawking ~ A^-1/2
Stefan-Boltzmann law
energy density ~ THawking^4 ~ A^-2
Total redshifted power
P ~ A (energy density) ~ A^-1
A ~ M^2
P ~ dM/dt
tlifetime ~ M^3
OK now my new prediction following the same argument as above
The redshifted thickness gravity Unruh temperature is
T' ~ (LA^1/2)^-1/2
If we take
Lp ~ mp = Planck mass
T' ~ (mpM)^-1/2
P' ~ AT'^4 ~ A/L^2A ~ L^-2 ~ mp^-2
dM'/dt ~ mp^-2
t' ~ mp^2M << t ~ M^3
Category: MyBlog

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