On Higher Derivative Gravity in Two Dimensions

Abstract

The 2D gravity described by the action which is an arbitrary function of the scalar curvature $f(R)$ is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function $f=R\ln R$ the model coupled with scalar (conformal) matter is exactly integrated and is shown to describe a black hole of the 2D dilaton gravity type. The influence of one-loop quantum corrections on a classical black hole configuration is studied by including the Liouville-Polyakov term. The resulting model turns out to be exactly solvable. The general solution is analyzed and shown to be free from the space-time singularities for a certain number of scalar fields.

24p., (5 figures, available upon request), JINR E2-94-185, Latex

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• Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
• The classical solutions of two-dimensional gravity
• Entanglement entropy and the Ricci flow
• Exact Solution of 2D Poincare Gravity Coupled to Fermion Matter
• Symmetric Variations of the Metric and Extrema of the Action for Pure Gravity
• Second Law of Black Hole Mechanics for all 2d Dilaton Theories
• Effects of Cuscuton dynamics on braneworld configurations in the scalar-tensor representation of $f\left(R,T\right)$ gravity