Paper detail

The Width Paradox and the Internal Structure of a Black-Hole

In the early days of Black Hole Thermodynamics, Bekenstein calculated the mass dispersion of a macroscopic black hole that results from the stochasticity of the thermal radiation it emits -- it turned out to be negative for black holes massive than $M \stackrel{>}{\sim} 10^{30}g$. He named it the {\it "mass width paradox"}. Here we revisit his early calculation, in an axiomatic approach with a set of more economical assumptions and reach similar conclusions. We argue that the mass paradox results from considering a black hole as a classical system, without an inner quantum structure. As a matter of fact, when we take into account the discreteness of the area levels and assume identical probability transition between contiguous quantum states \cite{bekenstein}, the paradox disappears. In the process we obtain the probability of finding a black-hole in some area eigenstate for a given averaged area. As a by-product, the quantum scenario also points towards a possible solution of the black hole information conundrum.