From: scerir (scerir@libero.it)
Date: Tue Dec 10 2002 - 16:17:28 MST
[Anders]
> Yes, this is very useful. But isnīt this extraction process only for the
> electrical part of the mass-energy? I thought it ended up with a boring
> schwarzschild hole after the charges had been neutralized.
Yep! Yes, as Bekestein noticed, the M-irr (the rest mass, minus
the gravitational potential energy, plus the kinetic energy
of the rest mass) is independent of the EM energy. So the
extraction process has to do with the total energy of the
EM field (including its gravitational binding energy),
that is to say with the term Q^2/2r, where Q is the charge,
and r is the radius of the external horizon of the EMBH.
If the total mass-energy M = (M-irr + Q^2/2r) > Q an EMBH
is formed.
> I thought it ended up with a boring Schwarzschild hole
> after the charges had been neutralized.
The pair creation process requires an electric field strengh
like (m^2 c^3) / (hbar e) where m and e are the mass and the
charge of an electron. But the key factor is that the number
of pairs (e+ e-) created is very high, something like
(Q x radius of the dyadosphere)/(e x Compton el. wavelenght).
This means that the density of pairs created, as a function
of the radial coordinate is so high (and the time so short) that
these pairs will leave the EMBH by creating an enormous pulse,
which expands relativistically out to infinity. Or, in a different
picture, the e+ e- plasma fluid expands, cools, and the pairs
recombine.
Is it possible to sketch a perfect EMBH engine based on
creation of pairs - expansion of plasma - compression -
annihilation? I do not think so because, imo, the EMBH must
lose some mass-energy, sooner or later.
Got the unpleasant feeling that all the above was 'murkily
written and murkily thought' :-)
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