Signatures of discretization in quantum black hole spectra

The quantum superposition principle states that quantum-mechanical systems such as atoms can be placed in a superposition of mass-energy eigenstates. Inspired by this idea and the seminal conjecture of Bekenstein, who proposed that black holes in quantum gravity must possess a discrete mass eigenspectrum, here we analyze the effects produced by a black hole in a superposition of masses. Analogous to using the electromagnetic field to probe atoms, we consider a quantum scalar field on the spacetime background sourced by the black hole mass superposition. From the resulting spectra, as measured by a hypothetical two-level system interacting with the field, we infer signatures of discretization of the black hole mass in support of Bekenstein's conjecture.