Statistical entropy of BTZ black hole in higher curvature gravity

For the BTZ black hole in the Einstein gravity, a statistical entropy has b een calculated to be equal to the Bekenstein-Hawking entropy. In this paper , the statistical entropy of the BTZ black hole in the higher curvature gra vity is calculated and shown to be equal to the one derived by using the No ether charge method, This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diff eomorphism invariant theories of gravity. A relation between the cosmic cen sorship conjecture and the unitarity of the conformal field theory on the b oundary of AdS(3) is also discussed. (C) 2000 Published by Elsevier Science B.V. All rights reserved.