We investigate the Brown-York stress tensor for curvature-squared theories.
This requires a generalized Gibbons-Hawking term in order to establish a
well-posed variational principle, which is achieved in a universal way by
reducing the number of derivatives through the introduction of an auxiliary
tensor field. We examine the boundary stress tensor thus defined for the
special case of `massive gravity' in three dimensions, which augments the
Einstein-Hilbert term by a particular curvature-squared term. It is shown that
one obtains finite results for physical parameters on AdS upon adding a
`boundary cosmological constant' as a counterterm, which vanishes at the
so-called chiral point. We derive known and new results, like the value of the
central charges or the mass of black hole solutions, thereby confirming our
prescription for the computation of the stress tensor. Finally, we inspect
recently constructed Lifshitz vacua and a new black hole solution that is
asymptotically Lifshitz, and we propose a novel and covariant counterterm for
this case.Comment: 25 pages, 1 figure; v2: minor corrections, references added, to
appear in JHE
