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 $\beta$, 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 $\eta$. 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.