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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.
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