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Hawking radiation on a falling lattice

Ted Jacobson·David Mattingly
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Abstract

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 $\sim0.08$ in units where the surface gravity is 1.

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Ted Jacobson, David Mattingly. 2000-01-12. Hawking radiation on a falling lattice. https://doi.org/10.1103/physrevd.61.024017

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