### Do Roche limits apply to black holes?

• Consider black hole A, a super massive black hole at the center of the galaxy. Orbiting it is black hole B, a much less massive black hole.

If some passing body were to modify black hole B's orbit such that it fell within the Roche limit of black hole A, what would happen to black hole B?

If it were to turn into a ring, would the black hole matter re-inflate since it wouldn't be under such high gravity? Do black holes even respond to Roche limits like regular matter does?

The idea of the Roche limit does apply to black holes if the secondary body *isn't* a black hole. For example, if an asteroid approaches a black hole too closely, it will be torn apart. The distance at which this happens is related to the radius of a body with the mass of the black hole and the density of the asteroid.

8 years ago

The Roche limit applies when a smaller body that would be held together by its own self-gravity is in the gravitational field of another, such that the tidal forces of the latter are stronger than the self-gravity of the latter, thus destroying the smaller body.

However, the gravitational tidal forces of a black hole are always finite, except at the internal singularity. This is a problem because the self-gravity of a black hole, in the sense of the acceleration a mass would need to remain stationary on its surface, is infinite1. Thus, we shouldn't expect for a large black hole to destroy another through gravitational tidal forces.

Put another way, the Roche limit occurs when particles from the smaller body can escape them... but they can't escape the event horizon of a black hole. Thus, the black holes will either orbit or merge, which is what happens in numerical simulations.

1There is a separate concept of surface gravity of a black hole that's essentially this re-scaled by the gravitational time dilation factor, and thus kept finite.