Energy and the Variational Principle in New Massive Gravity (NMG)

New Massive Gravity (NMG)---a particular massive theory of gravity that is fourth order in derivatives of the metric---formulated around a three-dimensional anti-de Sitter ($AdS_3$) background faces two major problems. In general, higher-derivative Lagrangians generate unwanted boundary terms that spoil the variational principle. Additionally, global charges---including the mass and angular momentum of black holes---diverge in asymptotically $AdS_3$ spacetimes in the absence of a well-defined renormalization procedure. This talk shows how both problems can be resolved with the addition of boundary terms to the action of new massive gravity.