Critical Gravity in Four Dimensions

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.

10 pages; New results on positivity of energy of logarithmic modes added, typos corrected, and clarifications made

References in corpus (5)

• Massive Gravity in Three Dimensions
• Note on New Massive Gravity in $Ad{S}_3$
• D-Dimensional Log Gravity
• Modes of Log Gravity
• On Hybrid (Topologically) Massive Supergravity in Three Dimensions

Cited by in corpus (9)

• Einstein Gravity from Conformal Gravity
• D-Dimensional Log Gravity
• AdS Waves as Exact Solutions to Quadratic Gravity
• Modes of Log Gravity
• On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions
• Ghosts of Critical Gravity
• Brief Note on AMD Conserved Quantities in Quadratic Curvature Theories
• Deeper discussion of Schrödinger invariant and Logarithmic sectors of higher-curvature gravity
• Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space