How do black holes orbit and merge in optical gravity?

https://en.wikipedia.org/wiki/No-hair_theorem

The name of the black hole no-hair theorem is misleading. Actually, it is a conjecture. It claims that after a black hole is formed, it can be described, for all practical purposes, with the mass, the angular momentum, and electric charge: that is, with just three real numbers.

Optical gravity, on the other hand, implies that the inside of the horizon is essentially frozen, but the Newtonian gravitational pull of the matter inside horizon can still be felt by an outside observer. Thus, the entropy of a forming black hole is large in optical gravity. We cannot describe a black hole with just three real numbers.

A problem in the optical gravity hypothesis is how do we model the merger of a binary black hole? LIGO has provided us with some empirical data of mergers.

In an optical black hole, the local speed of light inside the forming event horizon is zero. If we bring two black holes together, how do their forms adjust in the merger?

To explain the orbiting of two black holes, we have to add the following hypothesis to optical gravity:

Hypothesis 1. The local speed of light for signals between two spacetime points inside or close to the forming black hole horizon is essentially zero, but the forming black hole can move collectively and rotate collectively.


Hypothesis 1 is required by Lorentz invariance. If a horizon would stop and stick at "one position" in space, a black hole would have an infinite inertial mass.

Open problem 2. In optical gravity, what type of global transformations are allowed to deform the mass inside or near a forming horizon? Inside or very close to the horizon, the effective Newton or Coulomb force between masses that are close together, is essentially zero. All strictly local change has stopped from the point of view of a global observer. But there could be global deformations to the wave function of the system that still could happen and shape the insides of a forming horizon.


Open problem 2 exists also in traditional general relativity. We cannot map the proper time of an observer inside of the forming horizon to the proper time of an outside observer, because no signal can reach the outside.

If we have a cigar-shaped star and make a black hole out of it by collapsing a dust shell on it, does the cigar-shaped gravitational field persist or is it deformed to be spherical? If it becomes spherical, then an outside observer would see the mass inside the horizon to "move", but how can that happen if no signal can come out from inside the horizon?