The deformed two-dimensional black hole

TL;DR

This paper introduces a deformation of the wave equation on a two-dimensional black hole, modeling nonlocal effects that resolve classical singularities and allow wave propagation through regions previously considered singular.

Contribution

It presents a novel deformed wave equation that maintains well-posedness and resolves classical singularities in a two-dimensional black hole model.

Findings

Deformation allows wave propagation through the classical singularity.

Classical singularity is resolved by the deformation.

Wave-packets can reach another asymptotic region after deformation.

Abstract

A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal. The classical singularity present in the classical geometry is resolved by the deformation, so that propagation of a wave-packet can be continued through the classically singular region, ultimately reaching another asymptotically ``flat'' region.