It's a known result in thermodynamics. The amount of information that can be contained within a sphere of radius r is bounded by O(r^2), surprisingly. An object

It's a known result in thermodynamics. The amount of information that can be contained within a sphere of radius r is bounded by O(r^2), surprisingly. An object can attain this bound if and only if it is a Black Hole. This result is related to the fact that black holes evaporate. If black holes can contain information, it must be possible to read that information, or else it's observationally equivalent to the information having been destroyed. The evaporation of black holes leaks the information contained inside, avoiding a paradox.