John L.

2023-02-12 22:06:26 UTC

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]]