We reconsider the interrelation between the Schwarzschild radius and mass of
a spherical symmetric non-rotating and uncharged black hole. By applying the
relativistic mass-energy equivalence, the area of the horizon is expressed
independent of the Schwarzschild radius in terms of an occupation number
operator corresponding to the underlying many-body system of the particles
inside the black hole. Given the expectation value of the area in Fock space,
the von Neumann entropy based on the matter or radiation inside the black hole
is maximized to obtain the equilibrium probability density operator of the
underlying ensemble. We apply this approach to an ideal gas of
ultra-relativistic particles and to particles of rest mass zero. For both, the
entropy is expressed in terms of the horizon area of the black hole. In
addition, the quantum fluctuations inside the black hole are expressed in terms
of the standard deviation of the horizon area. The thermodynamic concept is
finalized by a generalized Planck law of the surface area which is derived at
the end.

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