Quantum portrait of a black hole with Pöschl-Teller potential

Abstract

We improve upon the simple model studied by Casadio and Orlandi [JHEP 08 (2013) 025] for a black hole as a condensate of gravitons. Instead of the harmonic oscillator potential, the Pöschl-Teller potential is used, which allows for a continuum of scattering states. The quantum mechanical model is embedded into a relativistic wave equation for a complex Klein-Gordon field, and the charge of the field is interpreted as the gravitational charge (mass) carried by the graviton condensate.