What are the effects of falling matter on a black hole and its event horizon?

[Skolon]

I have some questions about black holes (BH) for which I don't find until now any answer in what I read. I appreciate all answers.

1. When an observer that is out of BH influence are measure time elapse on a falling object he observe a "time dilatation" effect. What I don't understood is if that effect is asymptotically with event horizon (EH) BH or with its singularity. I mean, for the observer the falling object will be always visible or it will eventually disappear "beyond" EH?

2. The mass of BH is increasing just with rest mass of falling matter or the total kinetic energy of falling matter is added too? We can think that for an external observer in fact a collision never happen, so the kinetic energy can't be transferred to BH.

 

[Chalnoth]

I have some questions about black holes (BH) for which I don't find until now any answer in what I read. I appreciate all answers.

1. When an observer that is out of BH influence are measure time elapse on a falling object he observe a "time dilatation" effect. What I don't understood is if that effect is asymptotically with event horizon (EH) BH or with its singularity. I mean, for the observer the falling object will be always visible or it will eventually disappear "beyond" EH?

According to the outside observer, the infalling object gets closer and closer to the event horizon, with the light coming from the infalling object getting redshifted more and more. It is never observed to actually pass the event horizon, or disappear. It just gets redder and redder and more frozen in time.

2. The mass of BH is increasing just with rest mass of falling matter or the total kinetic energy of falling matter is added too? We can think that for an external observer in fact a collision never happen, so the kinetic energy can't be transferred to BH.

Well, think about it this way. If you have an infalling shell of matter, then from an observer outside the shell, the mass inside the shell doesn't change (Gauss's Law). As long as the shell remains spherically-symmetric, it doesn't matter what the configuration is, it will have the same shape.

But as this shell falls in, it will speed up. So clearly that kinetic energy, that came from the potential energy, cannot add to the mass of the black hole. We can look at this as the potential energy becoming negative as the kinetic energy becomes positive, so that the two don't matter when we consider how the mass looks like from the outside.

 

[clamtrox]

Kinetic energy is also completely dependent on the reference frame, while the mass of the black hole is not (as long as we are speaking about the real mass, not energy divided by c^2). I do think (but am not 100% sure) that 3-momentum is conserved when objects fall into a black hole.

 

[tiny-tim]

Hi Skolon!

1. When an observer that is out of BH influence are measure time elapse on a falling object he observe a "time dilatation" effect. What I don't understood is if that effect is asymptotically with event horizon (EH) BH or with its singularity. I mean, for the observer the falling object will be always visible or it will eventually disappear "beyond" EH?

Time dilation is 1/√(1 - 2M/r), where M is the mass and r is distance from the centre (this is in units with G = c = 1).

So this becomes infinite at r = 2M (the event horizon), and is meaningless for r < 2M.

2. The mass of BH is increasing just with rest mass of falling matter or the total kinetic energy of falling matter is added too? We can think that for an external observer in fact a collision never happen, so the kinetic energy can't be transferred to BH.

Of course, the black hole is also moving towards the object, just very much slower.

I think this is like two cars crashing head-on … all the KE disappears, but the energy has to go somewhere, and it goes into deforming the cars, plus noise and heat.

however, as clamtrox says, KE depends on the observer, and for the observer the object never actually reaches the event horizon, so the object and the black hole always remain separate.

The only relevant question the observer can ask (since he regards the the object as slowing as it falls) is, where is the KE going?

 

[Skolon]

Thank you for answers.

About kinetic energy: for a "normal" falling of matter (not on a BH) the KE is eventually transformed in other kind of energy (like radiation). Can we say that for an external observer the KE of falling matter on a BH is lost?
If yes, that mean that, at Universe scale, a huge amount of KE is lost "inside" black holes (especially when we take into account that almost all falling matter has relativistic velocity when it is "sucked" by BH).

About EH approaching falling matter: if for us (external observers) the falling matter is never cross the EH, when we are close enough to a BH can observe all BH history after its born? All that ever has fall down towards BH is visible (modified of course by red shifting effect)?