Gravitationally coupled Quantum Harmonic Oscillator

Abstract

We present a quantum harmonic oscillator model of a collapsed star trapped in the potential well of its gravitational field. The model incorporates quantum matter (quantum fields) as a source to classical gravitational field. We describe the gravitationally collapsed star as a quantum harmonic oscillator in an analogy with an electron trapped in a potential well. The subtle point we raise in this paper is whether a standard black hole scenario is a correct description for a gravitational collapse in a semi-classical framework.