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Abstract

Thermodynamics of local causal horizons have been shown to encode the
information necessary to derive the equations governing the gravitational
dynamics. We have previously shown that, in the presence of matter, this
derivation further implies quantum phenomenological corrections to
gravitational dynamics. Herein, we study whether similar corrections also occur
in vacuum. We show that, under the assumptions of locality and local Lorentz
invariance of physics, the vacuum dynamics is prescribed by the Einstein
equations. We also discuss an alternative paradigm which assumes the existence
of a preferred direction of time (much like in Einstein-aether or
Ho\v{r}ava-Lifshitz gravity). Then, we find an modified gravitational dynamics
in which Ricci curvature is sourced by Bel-Robinson super-energy.