Quantum Corrections to the Entropy of the Black Hole with a Global Monopole or a Cosmic String

The quantum corrections to the entropy of the static black holes with a global monopole or a cosmic string are studied by two methods: the brick wall and the Euclidean path integral. If we ignore the usual contribution from the vacuum surrounding the system, then the two approaches give the same results. The quantum corrections for the static black holes consist of two parts: One is quadratically divergent term which takes the geometric character. The other is a logarithmically divergent term which is not proportional to the horizon area. The renormalization of the quadratically and logarithmically divergent is also investigated.