Gravity from thermodynamics in vacuum: Lorentz invariance and the role of Bel-Robinson tensor

TL;DR

This paper explores how thermodynamic principles applied to local causal horizons can derive gravitational dynamics, showing that in vacuum Einstein equations hold under Lorentz invariance, but alternative theories involving Bel-Robinson tensors are also possible.

Contribution

It demonstrates that vacuum gravitational dynamics are governed by Einstein equations under Lorentz invariance and introduces a modified theory involving Bel-Robinson super-energy.

Findings

Einstein equations derived from thermodynamics in vacuum

Lorentz invariance leads to standard vacuum dynamics

Modified dynamics with Bel-Robinson tensor sourced Ricci curvature

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.