High School Black Holes: Questions on Event Horizon Observer

[kent davidge]

I have a doubt about black holes. (I'm sorrying for my poor English.):

1 - Does an observer outside a black hole see forever (i.e. his lifetime) a object stationary when it reaches the event horizon?

2 - Or photons emitted by the object have its wavelength so red-shifted that the observer essentially dont see the object anymore after an amount of time?

If (2) is the correct one, then why one say that objects never crosses the event horizon (from our pespective)? They might have crossed it but its photons are undetectable, because its too long wavelength. Obviously, that justification would be made taking no care about the other things we know from the theory. But just because we are not detecting photons from the object is not enough to decide if it has entered the black hole or not.

I appreciate any help.

 

[phinds]

I have a doubt about black holes. (I'm sorrying for my poor English.):

1 - Does an observer outside a black hole see forever (i.e. his lifetime) a object stationary when it reaches the event horizon?

Not quite but as close to stationary as to not be observably different as it shifts into invisibility.

2 - Or photons emitted by the object have its wavelength so red-shifted that the observer essentially dont see the object anymore after an amount of time?

Yes, exactly

If (2) is the correct one, then why one say that objects never crosses the event horizon (from our pespective)? They might have crossed it but its photons are undetectable, because its too long wavelength. Obviously, that justification would be made taking no care about the other things we know from the theory. But just because we are not detecting photons from the object is not enough to decide if it has entered the black hole or not.

The apparent speed of the object approaches zero as it approaches the EH so from the outside observer's point of view, it does not cross the EH.

 

[kent davidge]

The apparent speed of the object approaches zero as it approaches the EH

Thanks for replying. But yet the object disappear to the observer after some amount of time, right?

 

[Nugatory]

If (2) is the correct one, then why one say that objects never crosses the event horizon (from our perspective)?

#2 is indeed correct, and that claim about objects never crossing the event horizon from our perspective is pretty much wrong - you won't find it in any serious GR textbook.

It is correct to say that every event on the worldine of an external observer has a Schwarzschild $t$ coordinate equal to the $t$ coordinate of an event on the infalling object's worldline but still outside of the event horizon. That tells us a lot about Schwarzschild coordinates, but not much about anything else.

 

[Nugatory]

But yet the object disappear to the observer after some amount of time, right?

Right. A rather short amount of time too.

There are also two other unambiguously defined moments, and both of these happen fairly quickly:
1) The last moment that I, the outside observer, can send a message to the infaller and be able to get a reply indicating that the message was received.
2) The last moment that I can send a message that will be received by the infaller before they die at the central singularity.

 

[kent davidge]

Thank you very much Nugatory.