Black holes with a null Killing vector in three-dimensional massive gravity

We investigate solutions of new massive gravity with two commuting Killing vectors, one of which is null, with a special emphasis on black hole solutions. Besides extreme BTZ black holes and, for a special value of the coupling constant, massless null warped black holes, we also obtain for a critical coupling a family of massive ‘log’ black holes. These are asymptotic to the extreme BTZ black holes in the sense of log gravity.