*2.3. Body Entropy*

What happens to the entropy inside the black hole would be important to know (cf. [18] for a discussion of Hawking radiation inside black hole geometry) in order to resolve the puzzle. It is rather improbable that the entropy would be constant inside the black hole, as this would require that the interior is in thermal equilibrium, which it is certainly not when being under the conditions of collapsing matter under gravitational attraction. One might speculate that towards deeper inside, the entropy decreases with decreasing radius, because the surface decreases as <sup>∼</sup>(*r*/*RS*)2. Assigning a Hawking temperature to each shell of such a radius, the corresponding Hawking temperature would increase only as ∼*RS*/*r*. Thus any entropy-force potential should decrease towards the interior like ∼*r*/*RS*. The outer black hole horizon becomes the black hole shell of maximum entropy, the radius where the black hole entropy maximizes. The interior entropy force, the gradient of the potential, remains constant throughout the entire interior volume of the black hole with the exclusion of the singularity.

Notably, this entropy force points towards the interior of the hole, i.e., towards the singularity. It thus adds to the already existing gravitational acceleration being felt throughout the entire interior. By pointing inside towards decreasing radius *r*, it would push any existing massive particle that made it across the horizon into the singularity up in energy. This probably means that classically, no massive particle can make it across the horizon. It can only be non-massive radiation that crosses inward: photons and gluons, the massless bosons of electrodynamics and chromodynamics. Whether massive particles like electrons and quarks can indeed tunnel across the horizon remains a question that cannot be answered in the realm of classical physics.

Admittedly, these considerations are rather speculative as long as the evolution of entropy with increasing radial distance from the horizon towards inside and also outside the black hole has not been microscopically inferred. In any case, the question of the horizon representing a sharp surface remains a question that probably only quantum gravity can give an ultimate answer to, as it must proceed on scales close to the Planck scale *λP*. This is not our concern here.
