Scalar Fields In Curved Spacetime

Black hole is one of the predictions of Einstein's general relativity, but it is very hard to detect. 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. There also exists evidence of the presence of black holes in the center of our galaxy, and may be so in all galaxies in the universe. Nevertheless, these identifications have some ambiguities. 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. Once a field presents outside the black hole, it will affect the gravitational field, and vice versa. Even so, the existence of radiation, scalar or spinor, can still be assumed with its effect to the metric ignored, and only the gravitational effect taken into account. That is to say the radiation field should be taken as test field to study the properties it should possess.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 two chapters, the evolution of stars, concepts of black hole and the event horizon, the equilibrium between black hole and the exterior, Hawking radiation and scalar field radiation are introduced briefly.In chapter 3, the polynomial function is introduced to approximate the tortoise coordinate, and the numerical solutions of Klein-Gordon equation in Schwarzschild-de Sitter space-time are shown. These solutions can depict the...