  By applying the holographic renormalization method to the metric formalism of
f(Ric) gravity in three dimensions, we obtain the Brown-York boundary
stress-tensor for backgrounds which asymptote to the locally AdS3 solution of
Einstein gravity. The logarithmic divergence of the on-shell action can be
subtracted by a non-covariant cut-off independent term which exchanges the
trace anomaly for a gravitational anomaly. We show that the central charge can
be determined by means of BTZ holography or in terms of the Hawking effect of a
Schwarzschild black hole placed on the boundary.
