Final answer:
The moment of inertia of a black hole conveys meaningful information about its mass distribution inside and at the event horizon, and the hoop equivalence is not a meaningless coincidence.
Step-by-step explanation:
The moment of inertia of a black hole does convey meaningful information about its mass distribution, both inside and at the event horizon. The hoop equivalence, which states that for a rotating black hole, its moment of inertia is the same as that of a hoop with the same mass and radius, is not a meaningless coincidence. It is a result of the geometry and physics of rotating objects.
The moment of inertia is a measure of how mass is distributed in an object and affects how it responds to rotational motion. In the case of a black hole, the mass is concentrated at the singularity, which is a point of infinite density at the center. However, the event horizon, which is the boundary beyond which nothing can escape, also plays a role in the moment of inertia calculation.
For a non-rotating black hole, the mass is concentrated at the singularity and the moment of inertia is determined solely by the mass. But for a rotating black hole, the moment of inertia depends on both the mass and the distribution of mass inside or at the event horizon. The hoop equivalence arises because the distribution of mass in a rotating black hole can be effectively treated as if it were a hoop of the same mass and radius.