Finite gravitational action for higher derivative and stringy gravities - art. no. 064018

We generalize the local surface counterterm prescription suggested in Einst ein gravity for higher derivative (HD) and Weyl gravities. Explicitly, the surface counterterm is found for three- and five-dimensional HD gravities. As a result, the gravitational action for asymptotically AdS spaces is fini te and the gravitational energy-momentum tensor is well defined. The hologr aphic trace anomaly for 2D and 4D boundary (gauge) QFT dual to the above HD gravity is calculated from the gravitational energy-momentum tensor. The c alculation of the AdS black hole mass in HD gravity is presented with the a bove prescription. A comparison with the standard prescription (using refer ence spacetime) is done.