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Abstract: In this note we investigate the generalized massive gravity in asymptotically$AdS 3$ spacetime by combining the two mass terms of topological massivegravity and new massive gravity theory. We study the linearized excitationsaround the $AdS 3$ background and find that at a specific value of a certaincombination of the two mass parameters chiral line, one of the massivegraviton solutions becomes the left moving massless mode. It is shown that thetheory is chiral at this line under Brown-Henneaux boundary condition. Becauseof this degeneration of the gravitons the new log solution which has alogarithmic asymptotic behavior is also a solution to this gravity theory atthe chiral line. The log boundary condition which was proposed to accommodatethis log solution is proved to be consistent at this chiral line. The resultingtheory is no longer chiral except at a special point on the chiral line, whereanother new solution with log-square asymptotic behavior exists. At thisspecial point, we prove that a new kind of boundary condition called log-squareboundary condition, which accommodates this new solution, can be consistent.



Autor: Yan Liu, Ya-Wen Sun

Fuente: https://arxiv.org/







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