On the horizon entropy of a causal set
arXiv:2012.06212 · doi:10.1088/1361-6382/abe957
Abstract
We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.
arXiv comment26 pages, 9 figures. Updated to v2 to match the accepted manuscript
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