Brozos Vázquez, MiguelCaeiro Oliveira, SandroGarcía Río, Eduardo2022-09-282022-09-282022Brozos-Vázquez, M., Caeiro-Oliveira, S., & García-Río, E. (2022). Homogeneous and curvature homogeneous Lorentzian critical metrics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1-25. doi:10.1017/prm.2022.440308-2105http://hdl.handle.net/10347/29282We 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 Einsteineng© The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly citedAtribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Quadratic curvature functionalLorentzianCritical metricCurvature homogeneusHomogeneusRicci solitonjournal article10.1017/prm.2022.441473-7124open access