[boris]

Okay, I'm with you.

Can you elaborate on how the field changes as the hole absorbs new mass?

I.E. suppose a star falls into the hole, increasing its mass greatly. You are orbiting the hole at a nice safe distance. Does your orbital speed change? (Does the observed gravitational field of the hole change?) If so, how is the change communicated to the outside world?

Presumably by gravity waves. Eventually the field 'settles down' to its new value.

If the source of the field (the new, stronger one) is the event horizon, then the hole cannot appear as a "point source" of gravity (a particle) since the source is distributed. I'm thinking of Lambert's cosine law for radiation.

In other words, I am still confused and need instruction!

--Boris

[Physicist]

If the source of the field (the new, stronger one) is the event horizon, then the hole cannot appear as a "point source" of gravity (a particle) since the source is distributed.

Well, there you go. A spherical distribution of matter exhibits the same field, outside of the sphere, as would a point source of the same mass at the center of the sphere, by symmetry.

In any case, an object falling into a black hole, as viewed from the outside, takes an infinite amount of time to reach the event horizon, owing to the fact that the gravitational time dilation becomes infinite at the event horizon.

[Physicist]

Oops, I forgot to answer these:

I.E. suppose a star falls into the hole, increasing its mass greatly. You are orbiting the hole at a nice safe distance. Does your orbital speed change? (Does the observed gravitational field of the hole change?)

Yes and yes.

Gauss's Law applies to gravitational fields as well as to electromagnetic fields. Imagine the field as a bunch of lines that radiate outwards through space. The stronger the field, the more lines there are. If you draw some surface (say, a spherical shell) enclosing some region of space, and you want to know the integral of the field over that surface, it will be proportional to the amount of charge enclosed within that surface. (The "charge" in the case of gravity is simply the enclosed mass.) The more charge (mass) you throw into the enclosed volume, the more field lines will come out of the surface.

If so, how is the change communicated to the outside world?

All changes in the gravitational field would be communicated in the form of gravitational waves.