Sergey Bondarenko, Dima Cheskis, Raghvendra Singh

We have developed an effective thermodynamic model for a black hole's interior composed of scalar quasiparticles. The proposed interior consists of a core and a crust; the properties of both depend on the kinetics of the quasiparticles. In the core, the quasiparticles possess zero classical kinetic energy; the total potential energy $U(N)$ of the core depends only on the number $N$ of quasiparticles inside it. The thermodynamic description of this state of matter requires the introduction of an inverse temperature $\beta$ inversely proportional to $U(N)$ that supplants the standard temperature in every thermodynamic relation inside the core, driving both the energy density and the pressure negative. The different states of the core, correspondingly, can be parametrized by an additional parameter, which is a mean occupation number $\eta$ of the quasiparticles in the core. Concerning the crust, there are quasiparticles in it that remain trapped by the gravitational potential at finite temperature. The no-escape condition for the quasiparticles in the crust is imposed through a truncation of the phase-space integrals, yielding a direct and analytical coupling between thermodynamics and gravity. The resulting framework unifies core and crust within a single quasiparticle description, highlights the role of negative energy and pressure in black hole interiors, and provides testable predictions for any semiclassical theory that aims to resolve the singularity problem.