$\mathcal{PT}$ symmetry-protected exceptional cones and analogue Hawking radiation

TL;DR

This paper explores how parity-time-symmetric non-Hermitian Hamiltonians can model black hole horizons and Hawking radiation in analogue gravity systems, revealing tilted exceptional cones that mimic light cones near black holes.

Contribution

It establishes a connection between PT-symmetric dissipative Hamiltonians and analogue black hole horizons, demonstrating how exceptional points form cones analogous to light cones and analyzing tunneling processes related to Hawking radiation.

Findings

Exceptional points form tilted cones mimicking light cones near black holes

Tunneling processes analogous to black hole Hawking radiation are observed

Thermal contributions to analogue Hawking radiation are identified

Abstract

Non-Hermitian Hamiltonians, which effectively describe dissipative systems, and analogue gravity models, which simulate properties of gravitational objects, comprise seemingly different areas of current research. Here, we investigate the interplay between the two by relating parity-time-symmetric dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes emitting Hawking radiation. We show that the exceptional points of these Hamiltonians form tilted cones mimicking the behavior of the light cone of a radially infalling observer approaching a black hole horizon. We further investigate the presence of tunneling processes, reminiscent of those happening in black holes, in a concrete example model. We interpret the non-trivial result as the purely thermal contribution to analogue Hawking radiation in a Schwarzschild black hole. Assuming that our particular Hamiltonian models a photonic crystal, we discuss the concrete nature of the analogue Hawking radiation in this particular setup.