I was trying to imagine what would happen to a particle moving at
relativistic velocities as it approached a black hole from a great
distance. Obviously, it can't accelerate at the rate Newtonian physics
predicts, because it would exceed the speed of light well before it
reached the event horizon. The best I could come up with is that there
needs to be a factor of sqrt(1-v^2/c^2) applied to the acceleration,
as if gravity acted upon the rest mass. This seems to work out, but if
it were also true of particles moving away from black holes, there
would be no such thing as black holes, since the limit of the
gravitational drag would approach zero as the particle's velocity
approached the speed of light. This seems unlikely to me (though it
would explain why the big bang was not a black hole). Can someone help
me understand this?

Dear j.wesley.cleveland:
wrote in message
ps.com...
I was trying to imagine what would happen to a
particle moving at relativistic velocities as it
approached a black hole from a great distance.

Keep in mind that a black hole is like any other object... from
great disances. A black hole with the mass of the Earth is about
"1 inch" in diameter... so only 6400 km away, things would
accelerate pretty close to how they would accelerate near the
surface of the Earth.

Obviously, it can't accelerate at the rate Newtonian
physics predicts, because it would exceed the
speed of light well before it reached the event
horizon. The best I could come up with is that there
needs to be a factor of sqrt(1-v^2/c^2) applied to the
acceleration,

"Needs" is a pretty flaky reason. How about some theory...
http://people.hofstra.edu/Stefan_Wan...eom/Sec15.html
http://www.slac.stanford.edu/econf/C...s1/hughesI.pdf
.... plenty more on Google with:
formula velocity trajectory schwarzchild "black hole" site:.edu

as if gravity acted upon the rest mass.

Yes, speed does not affect rest or gravitational mass.

This seems to work out, but if it were also true
of particles moving away from black holes,

Starting where? Note that there is a whole Universe of particles
displayed around us that do not appear to be in black holes.

there would be no such thing as black holes,
since the limit of the gravitational drag would
approach zero as the particle's velocity
approached the speed of light.

There is your problem. As you approach a black hole, where your
speed is highest, there are fewer and fewer paths that mass can
follow, that do not point (eventually) into the event horizon.

This seems unlikely to me (though it would
explain why the big bang was not a black hole).
Can someone help me understand this?

The Big Bang was not a black hole because the early Universe had
matter fairly uniformly distributed across all of space. There
was no empty space into which the matter of the Universe was
flung.

David A. Smith