Quantum Portrait of a Black Hole with Pöschl-Teller Potential

Wolfgang Mück, Giancarlo Pozzo

Published 2014-03-06, updated 2014-03-13Version 2

We improve upon the simple model studied by Casadio and Orlandi [JHEP 1308 (2013) 025] for a black hole as a condensate of gravitons. Instead of the harmonic oscillator potential, the P\"oschl-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.