Two-oscillator Kantowski-Sachs model of the Schwarzschild black hole interior

TL;DR

This paper models the Schwarzschild black hole interior as a two-oscillator system, exploring classical, quantum, p-adic, and noncommutative cases, and analyzing its thermodynamics using the Feynman-Hibbs approach.

Contribution

It introduces a novel two-oscillator representation of the black hole interior and extends analysis to p-adic, noncommutative, and quantum frameworks, including thermodynamic properties.

Findings

Classical and quantum wave functions are derived.

Adelic wave functions are constructed.

Thermodynamics of the model is analyzed.

Abstract

In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model will be presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of the model, will be written, and then an adelic wave function will be constructed. Finally, thermodynamics of the model will be studied by using the Feynman-Hibbs procedure.