Re: Black hole questions

Wai Yu Wong wrote:
1. When a heavy object, say a neutron star, approaches a black hole,
will the black hole be moved by the gravity of the former?

Yes (accepting your loose terminology). The two objects will orbit around their common barycenter (assuming all other masses are very far away).

Far outside its horizon, a black hole acts like an ordinary object with the same mass. Near the horizon, however, a black hole is VERY different from an ordinary object.


If so, how
long does it take for the change of the black hole's gravity to reach
the object?

The question does not make sense. In GR, gravity does not "propagate", and asking about speed or "how long it takes to get there" is inappropriate. Changes in the gravitational field(s) propagate with speed c. In the rest frame of the black hole, in the approximation that everything else is either of negligible mass or very far away, its gravitational field is unchanging (until some massive object approaches and negates that approximation).


It seems to me that since it takes inifinite time for light both to
reach and escape from the event horizon, and that gravity travels at
the same speed as light, we can never observe the acceleration of a
black hole caused by another object's gravity.

This is wrong. The "gravity" of a black hole does not "propagate" from horizon to other locations, it just _is_.

If, for instance, you had a black hole of "mass" M near an ordinary star with mass 1,000,000*M, the black hole would orbit or fall into the star, without the star moving appreciably at all.


2. When an object falls straight into a black hole, its thickness will
approach zero as it nears the event horizon due to relativistic
contraction.

No. The object itself is unchanged.

Just as "time dilation" and "length contraction" of SR are purely geometric, so too is the effect you attempt to describe. Yes, in terms of the coordinates of a distant observer the radial thickness of an object approaches zero as the object approaches the horizon. But the object itself is unchanged -- this is purely geometric perspective (e.g. like this: a building is measured to be wider when measured directly from the front than from a corner, but the building itself did not change, the _projection_ of its width onto your ruler is what changed).


From the object's frame of reference, will the event
horizon appear elongated, flat or the same (spherical)?

It depends in detail how an observer on the object tries to observe the horizon. Note that the horizon is just a geometrical locus, and in general there is nothing there to identify it. Indeed, an infalling observer cannot locate the horizon via local measurements of any kind, it requires global observations to identify the horizon (e.g. from the behavior of images of distant stars, which act bizarrely near the horizon).


From a distant observer's frame of reference, the thickness of the
object will be less than the size of an atom nucleus before it crosses
the event horizon. From the object's frame of reference, does an atom
nucleus appear thicker or the same? Or has GR broken down already?

An observer on the infalling object making purely local measurements (e.g. inside a space ship) notices nothing unusual when near or crossing the event horizon of a black hole much larger than the ship. Including measurements of atoms comprising the ship or its contents.

Attempts to measure distant objects will depend on precisely how those measurements are performed, and can be bizarre near the horizon.


3. When a heavy object touches a black hole's event horizon, the
space-time curvature of that point will be reduced by the gravity of
the former, and thus it is no longer part of the event horizon.

Hmmm. The event horizon is an abstract locus, and is not a fixed property of the black hole. It is just the boundary between two spacelike regions: from outside the horizon it is possible for timelike and null objects to escape to spatial infinity, and from inside it is not. But there is no visible "border" or "fence" present there, and as I said above, this locus cannot be discovered by local measurements.

When another massive object approaches the horizon, the horizon becomes distorted by its presence. When the object gets close enough, the horizon moves with local speed c to surround the object -- as soon as that happens the object will inevitably be drawn into the black hole and cannot escape. The black hole will oscillate, as will its horizon, emitting gravitational and perhaps other radiation; after it settles down (a finite time), the black hole will have no "hair" -- that is, its only intrinsic properties visible from outside its horizon will be its "mass", angular momentum, and charge.


Kip Thorne, _Black_Holes_&_Time_Warps_, is a non-mathematical discussion of the properties of black holes and other "outrageous" aspects of GR.


Tom Roberts
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