Geometric character of black-hole entropy

The geometry of the neighborhood near an event horizon is similar to the Ri ndler metric, which leads to the thermal effect of black holes. The entropy of the scalar field and the Dirac field are calculated in the black-hole b ackground. The entropy of the scalar field, which is proportional to the ar ea of the event horizon, is naturally derived. Under the condition of large -mass black hole, the entropy of the Dirac field is still proportional to t he area of the horizon. These results can be applied to a large class of bl ack holes. A new method for calculating the black hole entropy is proposed which makes it easy to calculate the entropy of a high-spin field in the bl ack-hole background. We also consider extreme black holes and point out tha t the topological entropy only has classical meaning.