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

TL;DR

This paper demonstrates the existence of nontrivial vacuum black holes and gravitational waves in three-dimensional f(R) gravity, challenging the trivial geometries of pure Einstein gravity and showing new dynamical solutions.

Contribution

It introduces the first vacuum black hole with nontrivial geometry in 3D f(R) gravity and constructs exact solutions for gravitational wave radiation and absorption.

Findings

Existence of vacuum black holes with singularities in 3D f(R) gravity

Presence of perturbative and exact gravitational wave solutions

Invalidity of Birkhoff-like theorem in this context

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.