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...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2003.04106 |