  We use the counterterm subtraction method to calculate the action and
stress-energy-momentum tensor for the (Kerr) rotating black holes in AdS_{n+1},
for n=2, 3 and 4. We demonstrate that the expressions for the total energy for
the Kerr-AdS_3 and Kerr-AdS_5 spacetimes, in the limit of vanishing black hole
mass, are equal to the Casimir energies of the holographically dual
n-dimensional conformal field theories. In particular, for Kerr-AdS_5, dual to
the case of four dimensional N=4 supersymmetric Yang-Mills theory on the
rotating Einstein universe, we explicitly verify the equality of the zero mass
stress tensor from the two sides of the correspondence, and present the result
for general mass as a prediction from gravity. Amusingly, it is observed in
four dimensions that while the trace of the stress tensor defined using the
standard counterterms does not vanish, its integral does, thereby keeping the
action free of ultraviolet divergences. Using a different regularisation scheme
another stress tensor can be defined, which is traceless.
