> Assuming that c is the limit speed for data transfer, galaxy brains have
> an obvious problem - it takes some 100K years for a message to get to
> all parts of a galaxy. The darn things are just too big and too diffuse!
Well, that depends on the scale. Their thinking could just as well
exist on different timescales, with quick subminds being isolated
from each other, seeing each other as individuals, and higher level
slower subminds gradually merging.
> The area of a black hole's event horizon is proportional to its mass.
> The more massive a balck hole, the less dense it is, and the smaller the
> gravitational field at the event horizon. Imagine building something
> like a dyson sphere whose radius is just slightly larger than the event
> horizon of a black hole of the same mass.... The kind of technology
> capable of a galaxy brain should be able to move all the matter in the
> galaxy essentially at will.
True, although it will take a long time (many millions of years, at
least), judging by Dyson's calculations.
> The gravity experts will have to answer the next speculation - since the
> gravity field within a spherical shell is flat, it may be possible to
> have an event horizon for the entire structure slightly below the
> orbits, and still maintain a black hole in the very center - provided
> gratis by most galaxies anyway....
>
> I don't know the numbers here, I guess that such an object will be a few
> tens of light years across - but about 10^4 times faster signaling.....
Sounds reasonable, beautiful and tricky (but feasible!) to design.
Note that you will have to take GR into account for the orbits;
making them interlace is a very nontrivial problem. Basically the
gravitational field ar radius r will be the black hole + all beads at
lesser radii, which creates a potential on the form
P(r)= -g Mb / r r<ri
P(r)= -g(Mb / r + (Ms / (ro - ri))(1 - ri/r))) ri < r < ro
P(r)= -g(Mb + Ms) / r r>ro
(if you calculate classically, which you can't do here :-), where Mb
is the black hole mass, Ms the shell mass, ro the outer radius and ri
the inner radius of the shell. I haven't taken different densities at
different radii into account.
Hmm, this looks odd. There is a dip in the potential inside the
shell. This suggests that self-gravity might be a big problem if the
shell is massive (the classic dyson sphere is not massive compared to
the central star). This dip might make orbits much trickier to
design, although a fun possibility is having a shell of equal mass to
the black hole orbiting between radii r=1 and r=2, g=1; it creates a
flat potential there - no tidal forces! Of course, I could have made
a simple mistake (and never trust a classical calculation!).
-----------------------------------------------------------------------
Anders Sandberg Towards Ascension!
nv91-asa@nada.kth.se http://www.nada.kth.se/~nv91-asa/main.html
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