  We calculate the difference of one-loop vacuum energies for massive scalar
field in five-dimensional AdS black hole. (The same is done in five-dimensional
deSitter space). In each case this difference is specified by the boundary
conditions corresponding to the double-trace operator (massive term) and it
describes RG flow in the manner discussed by Gubser-Mitra for pure AdS space.
For AdS black hole there occurs instability which is the manifestation of the
Hawking-Page phase transition. For stable phase of AdS black hole as well as
for deSitter bulk, c-function found beyond the leading order approximation
shows the monotonic behaviour consistent with c-theorem.
