A naive vision of black holes (which is mine) is that their total energy is zero.

Let the total energy of an object be the sum of its mass energy, its electric energy, its rotating energy, and its gravitational energy.
The first three energies are positive, while the gravitational energy is negative.

But a total energy cannot be negative, so there exist a limit where the total energy of the object is equal to zero, and this is object is a black hole.

Of course, by equating the total energy to zero, you will find special values for the radius of the black holes, and you will find qualitatively that this radius is decreasing when a black hole is charged or rotating.
The meaning of this radius is that you cannot put any value of energy in a sphere of given radius, there is a limit.

So maybe you could apply the same (naive) logic with two black holes, by adding not only the individual energies of each black hole, but also the interacting energies between the two black holes.

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