Critical Gravity in Four Dimensions

Details Critical Gravity in Four Dimensions Critical Gravity in Four Dimensions

2011-01-10

arxiv.org/abs/1101.1971v3

Phys.Rev.Lett.106:181302,2011

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevLett.106.181302

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.

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