Homogeneous solutions of minimal massive 3D gravity

In this paper, we systematically construct simply transitive homogeneous spacetime solutions of the three-dimensional minimal massive gravity (MMG) model. In addition to those that have analogs in topologically massive gravity, such as warped AdS and pp waves, there are several solutions genuine to MMG. Among them, there is a stationary Lifshitz metric with the dynamical exponent z = -1 and an anisotropic Lifshitz solution where all coordinates scale differently. Moreover, we identify a homogeneous Kundt-type solution at the chiral point of the theory. We also show that in a particular limit of the physical parameters in which the Cotton tensor drops out from the MMG field equation, homogeneous solutions exist only at the merger point in the parameter space if they are not conformally flat.