Critical Gravity in Four Dimensions

TL;DR

This paper explores a four-dimensional gravity theory with curvature-squared terms that becomes renormalisable and exhibits unique properties at a critical point, potentially serving as a simplified model for quantum gravity.

Contribution

It introduces a four-dimensional critical gravity theory that eliminates certain massive modes and analyzes its unique physical properties and potential as a quantum gravity toy model.

Findings

Massless gravitons have zero on-shell energy.

Logarithmic spin-2 modes have positive energy.

Black hole mass and entropy vanish in the critical theory.

Abstract

We study four-dimensional gravity theories that are rendered renormalisable by the inclusion of curvature-squared terms to the usual Einstein action with cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "New Massive Gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.