Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions.
The exact solution to geodesic equation in the braneworld black hole spacetime is found by method of Jacobian elliptic function, and the angle of perihelion precession is obtained by the zero point of Jacobian elliptic function for Mercury. Comparing numerical result with observation data, we give the value range of tidal charge.
The equation of state density is corrected by the generalized uncertainty principle. Statistical entropy of scalar field outside Reissner-Nordstrom black hole is computed by WKB approximation method. The result shows that this black hole entropy is proportional to its horizon area, which is the same as that given by brick-wall method. The difference from the brick-wall method is that the present result is convergent without any cutoff.Keywords Generalized uncertainty principle · Reissner-Nordstrom black hole · State density · Statistical entropy In recent 30 years, research on black hole has made considerable progress. The black hole theory collecting general theory of relativity, quantum theory and statistical thermodynamics into a body has become a hot spot in the research of current physics and astronomy. But people's understanding to the black hole entropy is actually not so satisfactory. Since the 1970s, Bekenstein and Hawking have proved that the entropy of black holes is directly proportional to the event horizon area [1, 2], and the statistical origin of black hole entropy has become an important subject in the research of theoretical physics. Because of the statistical significance of black holes entropy, the understanding to entropy involves its microscopic essence. Maybe a complete quantum gravitational theory is needed for us to truly understand microscopic origin of the black hole entropy. In present situation, quantum gravitational theory is not advanced enough and people develop a variety of semi-classic methods to explore microscopic origin of the black hole entropy. The common methods include brick-wall method, conical singularity, blunt-cone and volume cut-off, in which brick-wall method [3] proposed by 't Hooft in 1985 is most widely used. Although the conclusion that the entropy is proportional to the event horizon area has been obtained by brick-wall method, a cut-off has to be introduced to avoid divergence, which looks unnatural. Is there any other way that can be used to remove the divergence without any cut-off.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.