Critical metrics and massive gravity solutions on three-dimensional Brinkmann waves*

Abstract

Abstract Three-dimensional Brinkmann waves which are critical for quadratic curvature functionals are determined. Generically, if the metric is critical for some functional then it is critical for all of them. In contrast, there are four special functionals that do not share critical metrics with any other quadratic functional. It is also shown that these metrics provide explicit solutions for different massive gravity models.