| Black hole is a hot point of research in theoretical physics at present. Because of the extreme strong gravitational field and singularity structure of space-time, black hole appears to show some distinctive physical phenomena. In this paper, we studied the black hole entropy and the gravitational effect.In chapter 2, some efforts are attempted to resolve the black hole entropy of UV divergence.The number of quantum states of material field outside the black hole is divergent at the horizon by using usual state density equation, which is the original cause why black hole entropy diverges in Brick-Wall model. In recent years, the progress of superstring and loop quantum gravity indicate that spacetime is not continuous at the Planck scales. This discreteness will make some modification of the state density equation. The number of quantum states is convergent at horizon which is counted by using two different forms of modified density equation. And it solve the divergence problem in the Brick-Wall model.In chapter 3, exact solution of geodesic equation in spherically symmetric spacetime in general relativity is given by using elliptic function, and series expression of orbital precession angle is shown. In the case of weak field, the first term of this series is in accord with orther approximation mothod in textbooks on the problem of perihelion precession of mercury. This series is applicable to case of strong field. Several classical gravitational effect are studied in the braneworld black hole spacetime. Exact solution of geodesic equation, orbital precession angle, light deflection angle and radar echo delay are obtained.These effects are different from general relativity because of tidal charge Q . Although these deviations appear in the second-order and high-order terms, they can to be confirmed or falsified with the increased precision of astronomical observations. And a potential experimental verification program for the large extra dimensions is provided.
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