Hawking radiation on a falling lattice

Scalar field theory on a lattice falling freely into a (1+1)-dimensional black hole is studied using both WKB and numerical approaches. The outgoing modes are shown to arise from incoming modes by a process analogous to a Bloch oscillation, with an admixture of negative frequency modes corresponding to the Hawking radiation. Numerical calculations show that the Hawking effect is reproduced to within 0.5% on a lattice whose proper spacing where the wavepacket turns around at the horizon is ~0.08 in units where the surface gravity is 1.