# Re: Hole in a box

Date: Thu Feb 14 2002 - 09:50:03 MST

On Thu, Feb 14, 2002 at 02:46:03PM +0100, Eugene Leitl wrote:
>
> Problem with small holes is that there's a tradeoff between luminosity and
> blackbody wavelength. E.g. a 10 kK hole would radiate less than a 10 MK
> hole, but 10 kK radiation sans attenuation would be a lot easier to use
> with solid state photovoltaic devices.

Thermodynamically speaking, wouldn't higher frequencies be more
efficient? We have spent most work on photovoltaics at wavelengths close
to solar radiation, but I don't see why similar ideas can't be used for
higher frequencies. Hmm, beyond a certain range molecular matter of
course becomes rather fragile, but there might be some interesting
nuclear photovoltaics that catch gammas and use them to do charge
separation.

> It would be interesting to see whether you could use an artificial
> gas/dust atmosphere around a nanohole to both feed it/attenuate the
> radiation if it's a hot hole. Somebody please do the math.

You would end up with the Eddington luminosity if the gas was just
gravitationally attracted. I guess a slightly different luminosity would
result if it was instead pressured. From the Second Fount of Knowledge
(http://scienceworld.wolfram.com/physics/EddingtonLuminosity.html), I
get: L_eddington = 4 pi c G M m / sigma_T

Using the pressure P instead of gravitation we get: L = 4 pi r^2 c P /
sigma T; the r dependency means that if the hole is in equilibrium at
its horizon, gas outside will be at a higher pressure and crowd in. This
increases L, moving the equilibrium shell outwards. Seems the full
situation is going to require some more careful analysis of how P is
changed by the hole. Could very well become an unstable or otherwise
messily interesting problem...

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Anders Sandberg                                      Towards Ascension!