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However, it looks as though we need H ~ Gm/c^2 ~ 10^-56 cm to get T > 2mc^2 and this is problematical since it's much smaller than the Planck length Lp ~ 10^-33 cm.


It depends how close you are to it as a static LNIF.

Here is one important idea that Nick got hung up on.
The Newtonian surface gravity is
gNewton = c^2rs/r^2 ---> c^2/rs
rs = 2GM/c^2
However, that is not correct for GR we need the time-dilation factor g00^-1/2
g(r) = (c^2/rs)(1 - rs/r)^-1/2   ----> infinity at the black hole horizon for static LNIFs hovering outside it.
we see c^2/rs as rs/r ---> 0
The temperature of the Hawking thermal radiation that the static LNIF detects T = hc/rskB = hc^3/2GMkB
that Unruh cites is what we see far from the black hole where the static LNIF merge to LIFs as rs/r ---> 0
Similarly for the observer-dependent cosmic horizon
g(r) = c^2/^1/2(1 - / ^2)^-1/2
we are at r = 0, so we see T = hc/^1/2/kB
but a static LNIF distance H << /^-1/2 from the horizon sees
T ~ hc/^1/4H^-1/2kB^-1 
Of course a geodesic LIF falling through the horizon sees T = 0 because its covariant acceleration is zero.
The photon is a null geodesic LIF, but the virtual electron-photon pairs clamped to the relative horizon of that retarded photon emitted from r = 0 are static LNIF with covariant acceleration c^2/^1/4H^-1/2.
On Jan 29, 2011, at 11:09 PM, JACK SARFATTI wrote:
On Jan 29, 2011, at 10:49 PM, nick herbert wrote:
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Dear Abbie--
To whom should I turn for reliable information
concerning horizon radiation?
eager to learn
Nick in Boulder Creek
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Dear Nick in Boulder Creek--
You could start with Bill Unruh's clever, amusing, detailed, intelligent
investigations about what might happen at horizons. ...
Take a look at: "Dumb Holes: analogues for Black Holes" by Bill Unruh
http://rsta.royalsocietypublishing.org/content/366/1877/2905.full.pdf
Happy Valentine's Day, eager to learn
Abbie
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