Thermodynamics of Gamow states gravitationally bound to Reissner-Nordström black hole

Abstract

We study charged scalar quasibound states in the Reissner-Nordstrom black hole spacetime by combining analytic solutions of the Klein-Gordon equation in ultralight regime Mμ ≪ 1 with quantum resonance theory formulated in a rigged Hilbert space. The resulting complex frequency spectrum describes metastable modes, with the real part giving the energy and the imaginary part determining decay or growth rates. The quasibound states are naturally interpreted as Gamow states associated with an effective non-Hermitian Hamiltonian. Building on this spectral description, we develop a thermodynamic framework for the quasibound state as an open quantum system using the Friedrichs model. This construction yields complex, time-dependent thermodynamic quantities, including internal energy, entropy, Helmholtz free energy, heat capacity and heat susceptibility. Interestingly, although the quasibound state entropy may become negative temporarily, the total entropy, when combined with that of the central black hole, remains positive and consistent with the generalised second law.