Three dimensional bigravity

In this paper, we explore some features of $f–g$ theory in three dimensions. We show that the theory has both anti–de Sitter and de Sitter solutions, the wave solutions in both cases are also obtained. In particular, at a critical value of the coupling constant, we see that the model admits log gravity solutions, reminiscent of topologically massive gravity and new massive gravity. We have also studied a class of exact static spherically symmetric black hole solutions in the model.