Conserved charges for even dimensional asymptotically AdS gravity theories

Mass and other conserved Noether charges are discussed for solutions of gravity theories with locally anti–de Sitter (AdS) asymptotics in $2n$ dimensions. The action is supplemented with a boundary term whose purpose is to guarantee that it reaches an extremum on the classical solutions, provided the space-time is locally AdS space-time at the boundary. It is also shown that if space-time is locally AdS at spatial infinity, the conserved charges are finite and properly normalized without requiring subtraction of a reference background. In this approach, Noether charges associated with Lorentz and diffeomorphism invariance vanish identically for constant curvature space-times. The case of a zero cosmological constant is obtained as a limit of AdS space-time, where $\Lambda$ plays the role of a regulator.