Quantized area of the Schwarzschild black hole: A non-hermitian perspective

In this work our aim is to link Bekenstein's quantized form of the area of the event horizon to the Hamiltonian of the non-Hermitian Swanson oscillator which is known to be parity-time-symmetric. We achieve this by employing a similarity transformation that maps the non-Hermitian quantum system to a scaled harmonics oscillator. To this end, we consider the unconstrained reduced Hamiltonian which is directly expressed in terms of the Schwarzschild mass and implies a periodic character for the conjugate momentum (which represents the asymptotic time coordinate), the period being the inverse Hawking temperature. This leads to the quantization of the event-horizon area in terms of the harmonic oscillator levels. Next, in the framework of the Swanson oscillator model, we proceed to derive novel expressions for the corresponding Hawking temperature and black hole entropy.