Black holes and gravitational waves in three-dimensional f(R) gravity

Abstract

In the three-dimensional pure Einstein gravity, the geometries of the vacuum space-times are always trivial, and gravitational waves (gravitons) are strictly forbidden. For the first time, we find a vacuum circularly symmetric black hole with nontrivial geometries in $f(R)$ gravity theory, in which a true singularity appears. In this frame with nontrivial geometry, a perturbative gravitational wave does exist. Beyond the perturbative level, we make a constructive proof of the existence of a gravitational wave in $f(R)$ gravity, where the Birkhoff-like theorem becomes invalid. We find two classes of exact solutions of circularly symmetric pure gravitational wave radiation and absorption.

6 pages, minor corrections, to match the published version

References in corpus (7)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
• Minimal Massive 3D Gravity
• On the Generalized Massive Gravity in $Ad{S}_3$
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• Three-dimensional black holes via Noether symmetries
• Complete quasinormal modes of Type-D black holes
• Black Holes and Non-perturbative Gravitational Waves in $f(R)$ Gravity
• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes