Homogeneous and curvature homogeneous Lorentzian critical metrics

We determine all three-dimensional homogeneous and 1-curvature homogeneous Lorentzian metrics which are critical for a quadratic curvature functional. As a result, we show that any quadratic curvature functional admits different non-Einstein homogeneous critical metrics and that there exist homogeneous metrics which are critical for all quadratic curvature functionals without being Einstein.

Automated summary

We investigate three-dimensional homogeneous and 1-curvature homogeneous Lorentzian metrics critical to a quadratic curvature functional. We demonstrate that any quadratic curvature functional can have distinct non-Einstein homogeneous critical metrics and that there are homogeneous metrics critical to all quadratic curvature functionals without being Einstein.