Re: Black holes

["Paul Camp" <pjcamp@coastal.edu>]

Chris Jones writes:
> 1. If an observer fell into a black hole, would it be possible for
> him to miss the singularity and pass out the other side? Or perhaps
> go into orbit around it, within the event horizon? Ignoring
> differential gravitational forces of course.....
>
> 2. A nonrotating uncharged BH is a pretty idealised object. What are
> the effects of angular momentum and charge on its characteristics?
> Can anyone recommend a good reference for this, the books and
> articles I've looked at seem to dismiss it as a problem seemingly
> too difficult to compute to bother with!

These are actually related questions. If you are inside the event
horizon, you cannot ever go into an orbit. In a sense, space has
become timelike and time has become spacelike (they swap signs in the
metric) so you only get to go one way in space but you can go
backwards and forwards in time. If you look at the set of light cones
for an observer falling into a black hole, they become tangent to the
observer's world line at the event horizon.

However, if the black hole rotates then the singularity, while still a
point, acquires some of the properties of a torus -- you only fall in
if you approach along the black hole's equator. If you approach from
any other direction, you pass through freely (assuming your body is
pointlike, of course) and loop around inside the event horizon forever
or until you do approach along the equator. Your references are
correct in stating that it is an inordinately difficult problem ad you
are unlikely to find any references outside of a graduate level GR
text (e.g. Wald or Misner, Thorne and Wheeler). 

There is a stranger effect associated with rotating black holes.
Recall that changes in the geometry due to rotation can propagate no
faster than the speed of light so there is some dragging of inertial
frames around a rotating black hole which can have the effect of
scooting an infallinf observer transversely. There is a sense in which
an observer falling into a non-rotating bh reaches the speed of light
at the event horizon. If we add rotation, and hence transverse speed
as well as radial then relative to a distant observer the net velocity
will be observed to be faster than the speed of light. The region
outside the event horizon where this strange effect occurs is called
the ergosphere and it has some rather strange properties, as worked by
Roger Penrose around 1970. It is possible, for example, for a particle
to move within the ergosphere but outside the event horizon with less
energy than it would have at a great distance -- think of it as a
geometry surfer. This includes its own mass energy so in effect it
begins to behave as if it had a negative mass energy, again as
observed by a distant observer. Penrose pointed out that you can use
this negative mass to extract energy from the black hole. Allow it to
explode into two parts and allow one part to fall along one of the
negative mass orbits into the black hole. This reduces the mass of the
black hole and, consequently, the remaining piece is propelled out
with more energy than the original particle had on entering the
ergosphere. In the process, some spin is lost as well so the
ergosphere shrinks. It vanishes before the mass vanishes so we are
saved from the possibility of a naked singularity.


> 3. Dave Bowman's reply is very in-depth (thanks!). But how does it
> affect the idea that if 2 BHs were to merge, the event horizon
> afterwards would have an area equal to the sum of the two previous
> event horizons' areas?

Equal to or greater than, mostly greater than. The entropy of a black
hole is proportional to its surface area and so the area cna never
decrease. This was proved around 1973 by Jacob Bekenstein who
apparently promoted the possible equivalence with entropy so loudly
that Stephen Hawking, in a fit of pique, tried to disprove his idea
and ended up proving it by showing that black holes radiate as black
bodies.

Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
Conway, SC   29526              variety in unity.
pjcamp@csd1.coastal.edu             --Umberto Eco
(803)349-2227                         The Name of the Rose
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