According to some sources an object traveling toward a black hole seems
to go slower and slower as it approaches. And that eventually it appears
to stop at the event horizon. Perhaps my understanding of this is wrong.
But if that's what happens, how does anything get into a black hole? They increase in mass over time, yes?

[[Mod. note --
Let's start with the simplest case: a non-rotating (Schwarzschild) black
hole (BH), and an object falling radially inwards towards the BH (so that
the object has no angular momentum about the BH). And let's equip the
falling object with a light/radio transmitter so observers can monitor
its position.

Based on the light/radio signals, a distant observer will "see" the
object's infall appear to slow down and eventually "freeze" just outside
the BH's horizon. The light/radio signals will also get more and more redshifted.

But this "freezing" is an optical/radio illusion: the object actually
continues to accelerate inwards, and falls in through the BH's horizon
in a finite time. The "freezing" is caused by the large gravitational
redshift of light/radio signals emitted by the object just outside the
horizon, taking a very long time to propagate outward to the distant
observer. (More precisely, that propagation time approaches infinity
as the emission point gets closer and closer to the horizon.)

That is, if we imagine the infalling object emitting period light/radio flashes, as the infalling object gets close to the horizon the flashes
take longer and longer to propagate out to a distant observer, and are
more and more redshifted in the process. Once the object passes through
the horizon, its light/radio signals don't get out to the distant observer;
the distant observer sees only those signals emitted before the object's horizon crossing.


For the more general case where the BH is spinning, everything above is
still true, but the mathematics is more complicated (the infalling object's path won't stay radial unless it's falling in along the BH spin axis).
If the infalling object has angular momentum about the BH, then (depending
on the details) it may orbit the BH and not actually fall in.

There's a nice discussion of falling-into-a-BH in the physics FAQ at
https://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html#forever
-- jt]]

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jt writes:
|But this "freezing" is an optical/radio illusion: the object actually

How is it an "illusion"? As I understand causality,
an event can only influence events in its future light cone.

So, where's the future light cone of the event "the faller
crosses the event horizon here"? This future light cone does
not seem to be in the space outside of the event horizon!

This would have the very real effect that this event cannot
influence anything in the space outside of the event horizont,
which is not an illusion.

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On Wednesday, February 15, 2023 at 7:47:38 AM UTC-6, Stefan Ram wrote:

jt writes:
|But this "freezing" is an optical/radio illusion: the object actually
How is it an "illusion"? As I understand causality,
an event can only influence events in its future light cone.

So, where's the future light cone of the event "the faller
crosses the event horizon here"? This future light cone does
not seem to be in the space outside of the event horizon!

This would have the very real effect that this event cannot
influence anything in the space outside of the event horizont,
which is not an illusion.

A better way of saying this is that you need to look at a Kruskal
diagram (there is a good one on Wikipedia). The event horizon is
along the positive speed of light line for the physical universe.
Note that the time-like hyperbolae accumulate as you get closer to
the event horizon. To reach the event horizon you must cross ever
more curves of constant time. To an outside observer the object
never truly reaches the event horizon since it can only do so in
the limit as time approaches infinity.

In the frame of the observer, this does not happen. They are pulled
in by the normal gravitational forces/spacetime curvature as for
any other object.

George


[[Mod. note --
There's a great discussion/explanation in figure 32.1 (pages 848-849)
of Misner, Thorne, and Wheeler's classic graduate general-relativity
textbook "Gravitation: (W. H. Freeman, 1973).

There's also a nice discussion/explanation in the first answers at
https://physics.stackexchange.com/questions/173554/formation-of-the-event-horizon-seems-impossible-with-singularity-inside-seems-im/173638#173638
But there are, alas, some quite bogus answers farther down on that page.
-- jt]]

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