http://meta-phys-thoughts.blogspot.fi/2018/04/how-do-black-holes-orbit-and-merge-in.html
The frame-dragging phenomenon of a black hole offers a solution. In optical gravity, a moving mass drags the optically dense medium along with it.
https://en.wikipedia.org/wiki/Frame-dragging
Close to the horizon of a black hole, the local speed of light as seen by a faraway observer can be arbitrarily slow. But the black hole can still rotate fast or move linearly fast relative to the distant observer. If the distant observer lowers a rope close to the horizon, the local speed of the rope relative to the black hole cannot exceed the local speed of light. The rope must be dragged along with the horizon. Close to the horizon, everything must move in the direction of the global movement of the horizon.
Similarly, if we have a glass sphere of a very high optical density, a ray of light that enters the ball must move along the ball.
What does frame-dragging say about the merging of two black holes? It is like two spheres of very high optical density colliding. The spheres are infinitely rigid because the local speed of light is essentially zero inside them. As soon as the horizons of the two black holes touch, their relative movement should stop. The result should be a dumbbell-shaped horizon.
The merged system will lose substantial energy in gravitational waves as the dumbbell keeps rotating. Does the horizon shrink because of the lost energy? It has to, because eventually the rotation will slow to a crawl and the combined ADM mass of the dumbbell is much lower than the sum of the masses of the original black holes.
As the horizon shrinks, parts of the old black holes will "melt". The local speed of light is greater than zero again in those parts. Thus, those parts can fall towards the new, smaller horizon.
What is the dynamics of the dragged space like in the collision of two black holes? In the center-of-mass frame the horizons of the black holes will appear squeezed in the direction of the movement. If the movement suddenly stops, what will the immediate shape of the horizon be?
What if we have a merger of two heavy neutron stars? The local speed of light is slow. The collision process has to happen like in a slow-motion film. The relative kinetic energy of the neutron stars will slowly be transformed into heat in their matter. Since the local speed of light is slow, the collision of the neutron stars is like two spheres of very viscous liquid colliding. The relative speed of the spheres can be high but the deformation of the spheres in the collision is necessarily slow.
The merger of two black holes colliding head-on should be like the merger of two infinitely viscous heavy neutron stars. Apparently, the relative kinetic energy of the matter in the black holes will remain kinetic energy after the collision, but since the local speed of light is essentially zero, there is no movement. The kinetic energy is kind of frozen in place.
The dumbbell will keep its shape after the contact of the horizons. If not much energy is lost in gravitational waves, the horizon will not shrink much. We are left with a dumbbell-shaped nonrotating black hole.
The creation of a dumbbell black hole can be viewed as a collision process that slows down infinitely at the first contact of the horizons.
What about a mini black hole that falls into a big black hole? Can it become infinitely squeezed at the big horizon? The length contraction is disturbed by the field of the mini black hole.
Conservation of momentum when the horizon reflects light
Our discussion above casts some light on the problem how a gravitational field can reflect photons. Where does the extra momentum go when a photon suddenly turns back in its path? The "viscosity" of the gravitational field may explain this. Since the gravitational field appears viscous to a faraway observer, it can absorb momentum from the photon. A black hole appears infinitely rigid and can easily absorb the extra momentum.
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