Fun with black holes
in [Relativity]
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From: Tom Roberts on 24 May 2010 02:11 Edward Green wrote: > The point is that the answer sounds like some kind of trick, whereas I > am proposing that the object never "really" penetrates the horizon, > for suitable values of "really". The lesson to be learned is that "reality" depends in essential ways on who is defining "reality". That's why the word "reality" is inappropriate here. A MUCH better way of discussing this is simply to realize that not every observer can observe what happens in every region of the universe. > Unless, that is, as something I have > read leads me to believe, the horizon eventually rises to meet the > infalling mass. Thereafter the black hole rings out like a bell until > the perturbation to its horizon has been absorbed. This is true -- the horizon ALWAYS expands outward to meet an infalling object. And the horizon ALWAYS relaxes afterward (becoming spherical if total spin is zero). > Black holes _can_ have hair, they just tend to go bald when they have > it. I believe the only type of "hair" possible is asymmetry, which relaxes down to the Kerr metric by emitting gravitational waves. Tom Roberts
From: Tom Roberts on 24 May 2010 02:14 eric gisse wrote: > Edward Green wrote: >> Unless, that is, as something I have >> read leads me to believe, the horizon eventually rises to meet the >> infalling mass. > > Uuuuuuhhhhhhh no. The horizon is a static fixture of the manifold. Not for the case of an object falling into a black hole from far away. >> Thereafter the black hole rings out like a bell until >> the perturbation to its horizon has been absorbed. > > No again. There is no analysis anywhere which supports this. Yes, there is. It's well known. But one must be careful in defining terms, because a distant observer cannot observe it. I believe it is discussed (in general terms) in the book by Kip Thorne I referenced earlier in this thread. Tom Roberts
From: Tom Roberts on 24 May 2010 02:18 Edward Green wrote: > Finite proper time either means it actually > falls in, or actually freezes. No. Finite proper time means a finite time to a comoving observer. An object that crosses the horizon in a finite proper time after a given point on its trajectory outside the horizon definitely DOES fall into the BH, according to a comoving observer. This is not "debatable". You seem to be hung up on the notion that any observer ought to be able to observe all aspects of "reality" -- that's quite naive. Tom Roberts
From: Tom Roberts on 24 May 2010 02:20 eric gisse wrote: > Edward Green wrote: >> MTW p.886 >> >> "When matter falls down a black hole, it can excite the hole's >> external spacetime geometry into vibration. The vibrations are >> gradually converted into gravitational waves..." > > Which does not mean the horizon itself changes. But it does do so. Tom Roberts
From: Tom Roberts on 24 May 2010 02:42
eric gisse wrote: > Once the matter is redshifted into oblivion it is a part of the black hole > as far as external observers are concerned. Yes. > As for the horizon _growing_ before the matter reaches it, nonsense. The > horizon will only grow in response to further input of mass-energy. No. Here's proof: Consider a Schw. black hole of "mass" M, and an infalling thin spherical shell of mass m that is initially far outside the horizon. Initially the horizon is essentially at r=M, but everywhere outside the shell the geometry is that of a black hole with "mass" M+m [#]. As the shell approaches the horizon, the horizon expands outward with local speed c, and the horizon and shell meet when both reach r=M+m together [#]. [#] Birkhoff's theorem. Heuristically this can be understood by considering spatial points between r=M and r=M+m, as the shell approaches. At some time before the shell actually reaches r=M+m, each such point must be inside the horizon, because an emitted light ray cannot reach r=M+m before the shell reaches r=M+m. We know [#] that when the shell reaches r=M+m the horizon must be at r=M+m. Yes, I am speaking a bit loosely here. > The event horizon is isn't a membrane. It is not a material surface. It is > not 'there'. Nothing special happens when something passes through it, other > than the certainty of never leaving the black hole. Yes to all that. But the horizon is a geometrical locus, and when spacetime is foliated into space and time, the spatial locus at a given time can change over time. Tom Roberts |