Re: What is a naked singularity...

Normally, when talking about black holes we mean a spherically-symmetric 
static system.  In that case, at the very center of the black hole,
the strength of the gravitational field becomes infinite, and the 
Einstein equations break down.  This mathematically singular point is 
surrounded by a region where light can't escape.  The outer limit of this 
region is called the event horizon, and we usually refer to anything inside 
the horizon as the black hole.  While physicists would normally be worried
about equations becoming singular, in this case we know that the Einstein
equations need to be extended to include quantum-mechanical effects when
studying the small region near this singular point, and the fact that
this singular point is effectively shielded from the rest of the universe
by the horizon.  For a long time is was assumed that any singularity that
would develop in general relativity would be covered by a horizon.

Today, through numerical techniques and newer analytic methods we can study
highly dynamic, non-spherically-symmetric systems.  In this case we
usually don't talk about the event horizon, but rather the apparent horizon.
Recently, there have been cases found where singular points can exist
without being shielded by a horizon.  These unshielded singularities are called
naked singularities.

I do not believe that there is any way to make a naked singularity into
a time machine.  More promising candidates for time travel are wormholes,
or two black holes connected together.  In that case, it looked for a while
that it would be possible to theoretically construct such a wormhole so
that a person could travel inside one hole and emerge outside of the other
without being harmed.  I want to emphasize that this is a game that scientists 
were playing just to see what was theoretically possible.  The technology
that it would take to construct such a thing seems highly unlikely to
ever exist.  More recent theoretical work in this area suggests that it
would in fact be impossible to construct such a thing.