Black holes and optimum coding

Abstract

A black hole (BH) communicates information about its event area to an observer. This defines an information channel. We show that if the area is optimally encoded, the probability law on its square root follows approximate exponential decay, and the resulting entropy is precisely the Bekenstein–Hawking result including the important factor of 1/4. This result arises as well as the solution to: (a) maximum entropy subject to a fixed message length, or (b) minimum Fisher information subject to a normalization condition. A verifiable prediction is a randomly enlarged event area, implying a randomly enlarged irreducible mass value. These effects should be observable as an enhanced number of BH's with large mass, resulting in an increased occurrence of gravitational lensing, and an enhanced ability to entrap relatively distant stellar objects.