Modeling an internal structure of a black hole using a thermodynamic quasi-particle model

We develop an effective thermodynamic model for a black-hole interior composed of scalar quasiparticles. The interior is represented by two regions: a dense core and a surrounding crust, whose properties are controlled by the quasiparticle kinetics. In the core, quasiparticles are assumed to have vanishing classical kinetic energy, so the total core energy is dominated by a potential-energy functional U (N) that depends only on the quasiparticle number N. As a consequence, the appropriate intensive variable governing the core thermodynamics is an inverse-temperature--like parameter β, introduced as the thermodynamic conjugate to U; it replaces the usual kinetic temperature T in the core equations of state and can drive the core pressure and energy density negative in the relevant regime. Different core states are further characterized by the mean occupation number η. In the crust, quasiparticles remain trapped at finite kinetic temperature, and the no-escape condition is implemented via a truncation of the phase-space integrals, yielding an explicit analytic coupling between thermodynamics and gravity. The resulting framework provides a unified quasiparticle description of core and crust, clarifies the thermodynamic origin of negative pressure/energy in the interior, and provides an effective thermodynamic setting for exploring how semiclassical or microscopic resolutions of the singularity problem might be constrained.