Field Equation In Curved Spacetime

Black hole is one of the predictions of Einstein's general relativity, but it is very hard to detect because the characters of black holes. People found compact objects in some binary systems, and identified them as black holes, because careful analysis showed that their masses are far beyond any limit accepted for dead stars in general relativity. If black holes have some characteristic radiation outside the event horizon, then a high precision can be expected to identify them and also to understand their inner structure.This dissertation is mainly about the scalar field in curved black hole spacetime backgrounds assumed to be asymptotic de Sitter space at infinity. In the first chapters, the concepts of black hole and the event horizon, black hole radiation ,the thermal properties of black hole, and scalar field radiation are introduced briefly.In chapter 2, the real scalar field equation is solved numerically in Schwarzchild-de Sitter space-time with different angular frequency co. A method called 憄olynomial? approximation is used to derive the relation between the tortoise coordinate x and the radius r. It抯found that the wave function is close to that of a harmonic wave. And when co alters, the curve抯amplitude and wavelength are different. The method of calculating the reflection and transmission coefficients is also discussed in this chapter.In chapter 2, the analytic solution of massless field equation in Kerr-Newman-de Sitter Spacetime which is given by Hisao Suzuk, Eiichi Takasugi and Hiroshi Umetsu is introduced. The Teukolsky equation is transformed to Heun eqution by variable substitution, and the Heun eqution is a known mathematical function, its solutions is in the form of series of hypergeometric functions. This method is helpful for us to find the way of the analytic solution of scalar field equation.