Re: Black hole evaporation (Violation of the second law of Thermodynamics)

From: Frank Hellmann (Certhas_at_gmail.com)
Date: 03/29/05 

Date: Tue, 29 Mar 2005 08:20:27 +0000 (UTC)

Jimi wrote:
> This may seem like a stupid question but if black holes radiate, and
> smaller black holes radiate faster, could a small black hole be used
> to convert mass into energy with 100% efficiency? What would be the
> drawbacks to this (besides the obvious of course)?

It radiates particles, so it's not 100% efficient however, imagine the
following Gedankenexperiment:

Set up a blackhole and a stable sphere of Temperature T<T_BH Take some
of the mass of the shell and drop it into the Black Hole, the Black
Hole will radiate out less (rest) mass at a higher temperature, which
can be absorbed by the shell in principle. Via this process the
temprature of the shell is increased at expense of it's (rest) mass. In
fact by letting the Black Hole radiate down to 1/M>>T The temperature
can be increased arbitrarily.

This is not overly shocking since this is semiclassical Black Hole
physics and classical Black Hole physics does not have well defined
Thermodynamic properties anyways (ergodicity trivially fails if a
particle falls into a black hole, equilibrium/adiabatic thermodynamics
can not be defined).

It's interessting to note that this could well be a property of
gravitating systems generally. Presumably a gravitating gas would not
spread out arbitrarily but tend to "lump" together. Something which at
first sight would violate the second law of entropy as well. Gravity
plays a central role in some "self organizing systems" (stretching the
term here) like convection.

These are all my own musings, does anyone know of any actuall research
into this direction? It would be appreciated.

c
Frank

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