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Feb 12, 2023, 5:06:30 PM2/12/23

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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]]

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]]

Feb 15, 2023, 8:47:38 AM2/15/23

to

jt writes:

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

How is it an "illusion"? As I understand causality,
|But this "freezing" is an optical/radio illusion: the object actually

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.

Feb 18, 2023, 3:49:19 AM2/18/23

to

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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