Finite gravitational action for higher derivative and stringy gravities

We generalize the local surface counterterm prescription suggested in Einstein 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 finite and the gravitational energy-momentum tensor is well defined. The holographic trace anomaly for 2D and 4D boundary (gauge) QFT dual to the above HD gravity is calculated from the gravitational energy-momentum tensor. The calculation of the AdS black hole mass in HD gravity is presented with the above prescription. A comparison with the standard prescription (using reference spacetime) is done.