Some exact solutions of all f(Ricci) theories in three dimensions

Abstract

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form f(Ricci) that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.

25 pages, references added, presentation improved, version to appear in Phys. Rev. D

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• Generalized Black Holes in 3D Kerr-Schild Double Copy
• Kerr-Schild--Kundt Metrics are Universal
• On Exact Solutions and the Consistency of 3D Minimal Massive Gravity
• Bulk and Boundary Unitary Gravity in 3D: MMG${}_2$
• Weyl-gauging of Topologically Massive Gravity
• Asymptotically flat black holes in 2+1 dimensions
• Gravity Waves in Three Dimensions
• Electromagnetic Generalized Quasi-topological gravities in $(2+1)$ dimensions
• From Smooth Curves to Universal Metrics
• Holographically Viable Extensions of Topologically Massive and Minimal Massive Gravity?
• Born-Infeld Type Extension of (Non-)Critical Gravity
• Scattering in Topologically Massive Gravity, Chiral Gravity and the corresponding Anyon-Anyon Potential Energy
• Minimal Einstein-Aether Theory
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
• Instability of BTZ black holes in parity-even massive gravity
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling
• Solutions with pure radiation and gyratons in 3D massive gravity theories
• Massive Higher Derivative Gravity Theories
• Topologically Massive Gravity: Anyon Scattering, Weyl-Gauging and Causality
• Impulsive gravitational waves in general massive 3D gravity
• Aspects of three-dimensional higher-curvature gravities