re:Hole in a box

From: Eugene Leitl (
Date: Mon Feb 18 2002 - 02:56:01 MST

On Sun, 17 Feb 2002, Amara Graps wrote:

> Extropes,
> Might I ask to those proposing wild-ass schemes, to please spend
> some time doing some background reading about the objects for which
> you are embedding in your engineering feat ? Not spending time

Holes with some 10 g/s mass equivalent luminosity are not well described
in the literature.

> on those basic pieces (including doing your own math) makes the

Guilty as charged.

> whole shebang look like hand-waving silliness. Probably I'm being
> grumpy, but alot of this black hole stuff can be found in basic
> introductory astronomy texts.

Sure, Hawking blackbody emission max and total luminosity vs. hole mass
(the area of the event horizont is not an additional parameter in the
equation, right? it should be just the mass) should be easy enough to
derive and plot. Trying to predict the accretion in presence of such flux
even in pure hydrogen does not sound modellable with just the pocket

We're talking about homeostating a hole with few g/s mass loss via
gravitational accretion through a submicron orifice. In terms of
Joule-Thompson, luminosity of a few g/s material flux through a submicron
orifice is negligable. However, assuming above mass flow and fusable
substrate (protium, deuterium, tritium, maybe lithium) we should see
considerable fusion output in the accretion disk, adding luminosity to the
pure Hawking blackbody.

> >Actually, it would probably make sense to keep a 10 kK hole in an opaque
> >sphere pressurized with hydrogen. What is the power output at that
> >blackbody maximum, about that of a nuke?
> Main sequence stars balance radiation pressure with gravity. That's
> what the above physical scenario looks like to me. Not a black hole.

Well, the radiation pressure will be considerable, given that we're
talking about nuke luminosities in micron volumes.

> Black holes in real life suck in matter around it, which become
> ultra hot accretion disks.

Compression in the accrection disk in this case seems negligable.

> >You're the resident astrophysicist here.
> (who doesn't feel motivation these months to spend my limited
> off-hours on science activities. I'm sorry about that, Eugene.)

I wasn't of course expecting *you* to do my homework; god knows you're
busy. I was trolling for comments from other resident armchair physicists.

> I have no idea if "nano-sized black holes" scale like star-sized or

I haven't done the math, but I think it should be rather called a
microhole than a nanohole. Mea culpa.

> galactic-sized black holes (I'm not a black hole expert). The
> pre-collapse state would be pretty wierd for a nano-sized black
> hole, though. I'm not saying that it's not possible, but whoever is
> proposing it should have a physically plausible description.

It is weird. I think it requires nuke hydro code modelling to arrive at a
realistic description. The hole size might become prohibitively large to
reduce photonic pressure sufficiently, so that the total luminosity of a
single hole might become too low.

> To power the energy output of a quasar (10^{47} erg/sec), assuming
> an efficiency mass conversion via a swirling accretion disk of 10%,
> would require swallowing more than 10 M_solar per year.

We're talking roughly about a small to large nuke output of the entire
hole/accretion/fusion assembly.

> It's useful to examine the density of the object becoming a black hole.
> For a pre-collapse state (using Euclidean geometry), the mean density of
> the pre-black-hole object of mass M is: ~ ( 3 c^6 ) / (32 pi G^3 M^2).
> [assumine a volume of a sphere, with R equal to the Schwarzschild radius
> 2GM/c^2]

Thanks for the equation.

> >Would feeding the nanohole with dust at all make sense?
> I didn't read the beginning and intermediate posts regarding this
> problem, Eugene, so I don't know the conditions. I would guess that
> the lifetime of the dust particle would not be very long though,
> because you're immersing the dust in a high-energy shocked plasma
> (i.e. the accretion disk around the black hole)

I realized that the lifetime of a dust grain nearby a nuke is negligable.
I was thinking about attenuation of the Hawking and fusion output. One
might have to use high-velocity high-density (say, tungsten) pellets to
feed the hole instead of just relying on gravitation accretion of

> Amara

Thanks a lot for those references you ferreted out, despite being so busy.
Thanks again!


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