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

Understand

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.