Causal sets can approximate black hole horizons via discrete timelike curves and ladders tracing null geodesics, with a discrete expansion changing sign across the horizon in a 1+1D toy model.
Dowker, Causal sets and the deep structure of spacetime, in100 Years Of Relativity: space-time structure: Einstein and beyond, edited by A
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Towards black-hole horizons and geodesic focusing in causal sets
Causal sets can approximate black hole horizons via discrete timelike curves and ladders tracing null geodesics, with a discrete expansion changing sign across the horizon in a 1+1D toy model.