Thermodynamics of analogue black holes in a non-Hermitian tight-binding model

We present a non-Hermitian model with gain/loss and non-reciprocal next-nearest-neighbor hopping that emulates black-hole physics. The model describes a one-dimensional lattice with a smooth connection between regions with distinct hopping parameters. By mapping the system to an effective Schwarzschild metric in the Painlev\'e-Gullstrand coordinates, we find that the interface is analogue to a black-hole event horizon. We obtain emission rates for particles and antiparticles, the Hawking temperature, the Bekenstein-Hawking entropy, and the mass of the analogue black hole as a function of the interface sharpness and the system parameters. An experimental realization of the theoretical model is proposed, thus opening the way to the detection of elusive black-hole features.