Re: Sphere of light around a black hole?

Maybe, but not as you describe.

To understand this, we first have to understand the photons are
NEVER at rest.  This is sort of a hard thing to explain if you don't
have some background in relativity, so I'll do my best here and if
you have further questions, feel free to email me.  So, Special
Relativity tells us that all inertial observers (those that are not
accelerating) measure the speed of light to be the same, regardless
of their relative velocities.  In other words, there is no way that
you can put yourself in a reference frame in which you will measure
the speed of a photon to be anything other than ~300,000,000 meters
per second, not to mention zero.

So what does this have to do with a black hole?  General Relativity,
the theory of gravity which explains how spacetime is warped by
the presence of matter (more precisely, any kind of energy), is
really an extension of Special Relativity.  One way to think of this
is as follows: even though the spacetime around a black hole is curved,
one can (except at the singularity in the center) always look at some
very small region which is very nearly flat.  An analogy is magnifying
a circle.  If you zoom in on the edge of a circle, at some point it
begins to look more and more like a straight line.  "Approximately
flat" spacetime means that within that small region, the symmetries
and transformations of Special Relativity, as well as their implications,
hold true.

Let's then consider an intrepid astronaut, Rob, who has volunteered
to fall into a black hole.  We'll make the black hole very large, so
that at any given time (except near the singularity), the spacetime
Rob occupies will be approximately flat.  At the exact instant Rob
crosses the event horizon, he shoots a laser radially outward (i.e.,
perpendicular to the event horizon surface).  We know from Special
Relativity that the photons will move away from him at the speed of light,
and not simply stick on the event horizon.

So that's a long way of giving a "no" answer.  The question then
arises as to what does happen to the photons from Rob's laser.
That's even harder to answer.  You may be familiar with the concept of
"redshift", which is the stretching of the wavelength of light.  Suppose
Rob fires his laser at regular (to him) intervals before he crosses
the event horizon.  His partner Fab, hovering at some distance away,
will see the wavelength of this light increasingly redshifted the closer
Rob gets to the event horizon.  In fact, though by Rob's watch the
laser is being shot at regular intervals, Fab will see the intervals
get longer and longer.  Now, Fab will never see the light fired exactly
at the event horizon, but by extrapolating his data from previous laser
shots, his explanation of this is that the light was redshifted to
an infinitely long wavelength.  This may seem strange, but part
of the reason for this is that "time" is wrapped up in "spacetime",
such that it's difficult to separate it from the space part in a
consistent way.  It's one of those seemingly bizarre situations that 
pop up a lot in relativity, precisely because measurements like this 
will change depending on what reference frame you are in.

Now it is in principle possible to make a "sphere of light" surrounding
the black hole.  To do this, though, you would shoot the photons
precisely *tangent* the the event horizon surface.  Then the photons
would orbit the black hole forever.  Of course this is an unstable
situation, since moving the photon an infinitessimal amount would
cause it to either fly away or fall into the singularity.  This in
turn brings up the funny question of how quantum mechanics factors into
all of this, since it seems to tell us that the position of the photon
is never definite.  Exactly how this folds back in to General Relativity,
which regards all positions as definite, is an area of active research.