New Exact Solutions of Quadratic Curvature Gravity

Abstract

It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in arbitrary dimensions in generic quadratic curvature theory. In addition to the AdS-wave (or Siklos) metric which represents plane waves in an AdS background, we present here a new exact solution, in this class, to the quadratic gravity in D-dimensions which represents a spherical wave in an AdS background. The solution is a special case of the Kundt metrics belonging to spacetimes with constant curvature invariants.

20 pages, references added, typos corrected, Appendix B improved, version to appear in Phys. Rev. D

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Cited by in corpus (19)

• AdS-plane wave and pp-wave solutions of generic gravity theories
• Generalized plane waves in Poincaré gauge theory of gravity
• Impulsive waves in ghost free infinite derivative gravity in anti-de Sitter spacetime
• Exact Solutions in Poincaré Gauge Gravity Theory
• Traversable Morris-Thorne-Buchdahl wormholes in quadratic gravity
• Born-Infeld Gravity with a Massless Graviton in Four Dimensions
• Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form
• Wave Metrics in the Cotton and Conformal Killing Gravity Theories
• A stationary axisymmetric vacuum solution for pure $R^2$ gravity
• Emerging Newtonian potential in pure $R^2$ gravity on a de Sitter background
• Minimal Einstein-Aether Theory
• Kerr-Schild-Kundt Metrics in Generic Einstein-Maxwell Theories
• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
• Instability of BTZ black holes in parity-even massive gravity
• The Exterior Calculus of Quadratic Gravity
• Revisiting Lifshitz-type solutions in $R^2$-corrected gravity
• Almost Universal Metrics
• Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories
• Kerr-Schild perturbations in higher derivative gravity theories in $D$ dimensions