Quantum simulation of rainbow gravity by nonlocal nonlinearity

TL;DR

This paper demonstrates how rainbow gravity, an energy-dependent modification of general relativity, can be simulated using nonlinear waves in nonlocal media, enabling experimental tests of quantum gravity concepts.

Contribution

It introduces a method to simulate rainbow gravity in laboratory settings using nonlinear wave equations in nonlocal media, bridging quantum gravity theories and nonlinear quantum physics.

Findings

Nonlocal nonlinear Schrödinger equation emulates curved spacetime near rotating black holes.

Superradiance and black hole instabilities are affected by energy-dependent metrics.

Experimental tests of quantum gravity theories become feasible in laboratory conditions.

Abstract

Rainbow gravity modifies general relativity by introducing an energy dependent metric, which is expected to have a role in the quantum theory of black holes and in quantum gravity at Planck energy scale. We show that rainbow gravity can be simulated in the laboratory by nonlinear waves in nonlocal media, as those occurring in Bose-condensed gases and nonlinear optics. We reveal that at a classical level, a nonlocal nonlinear Schr\"odinger equation may emulate the curved space time in proximity of a rotating black hole as dictated by the rainbow gravity scenario. We also demonstrate that a fully quantized analysis is possible. By the positive $\mathcal{P}$-representation, we study superradiance and show that the instability of a black-hole and the existence of an event horizon are inhibited by an energy dependent metric. Our results open the way to a number of fascinating experimental tests of quantum gravity theories and quantum field theory in curved manifolds, and also demonstrate that these theories may be novel tools for open problems in nonlinear quantum physics.