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Home Jack Sarfatti's Blog Blog (Full Text Display) What is the temperature of black hole and cosmic horizons really?

Jan
30

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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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