Non-Hermitian Hamiltonians, which effectively describe dissipative systems,<br>and analogue gravity models, which simulate properties of gravitational<br>objects, comprise seemingly different areas of current research. Here, we<br>investigate the interplay between the two by relating parity-time-symmetric<br>dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes<br>emitting Hawking radiation. We show that the exceptional points of these<br>Hamiltonians form tilted cones mimicking the behavior of the light cone of a<br>radially infalling observer approaching a black hole horizon. We further<br>investigate the presence of tunneling processes, reminiscent of those happening<br>in black holes, in a concrete example model. We interpret the non-trivial<br>result as the purely thermal contribution to analogue Hawking radiation in a<br>Schwarzschild black hole. Assuming that our particular Hamiltonian models a<br>photonic crystal of experimental relevance, we argue that the loss from the<br>latter in the form of thermal radiation can be interpreted as the blackbody<br>contribution to analogue black hole radiation when measuring at the exceptional<br>cone. As such, these systems are promising candidates for black hole analogue<br>models.
PT symmetry-protected exceptional cones and analogue Hawking radiation
Marcus Stålhammar,
Jorge Larana-Aragon,
Lukas Rødland,
Flore Kunst
We show that the exceptional surfaces of linear three-dimensional non-Hermitian parity-time-symmetric two-band models attain the form of topologically stable tilted exceptional cones. By relating the exceptional cones to energy cones of two-dimensional Hermitian parity-time-symmetric two-band models, we find a connection between the exceptional cone and the light cone of an observer in the vicinity of a Schwarzschild black hole. When the cone overtilts, light-like particle-antiparticle pairs are created resembling Hawking radiation. We also investigate dissipative features of the non-Hermitian Hamiltonian related to the latter and comment on potential realizations in laboratory setups.
