Quantum Scattering In Curved Spacetimes

Scattering by black holes is an interest topic in both black-hole physics and scattering theory. The presence of black holes can be inferred only through indirect methods. One of the most useful and e?cient ways to study the properties of black holes is by scattering matter waves from them.In Chapter 2,we study the absorption problem of a massless scalar ?eld propagating in general static spherically-symmetric black holes with a global monopole.By using a partial-wave method, we simulate the absorption cross section of a massless scalar ?eld propagating in general static spherically-symmetric black holes with a global monopole and analysis the physical information encoded in the sum over the partial-wave contributions.In Chapter 3,we numerically carry out the absorption cross section and?nd that the larger angular momentum quantum number l is, the smaller the corresponding maximum value of partial absorption cross section is. Comparing with Schwarzschild case, the absorption cross section of regular black holes is strengthened in both low and high frequency regions, and the absorption cross section oscillates around the geometric optical value in the high frequency region.Generally speaking, the scattering ?ux is strengthened and its scattering width becomes narrower in the forward direction.There are obvious contrast of scattering properties of di?erent type of regular black hole.In Chapter 4,we investigate the absorption of Dirac ?eld from the Bardeen regular black hole. We numerically carry out the absorption cross section, we?nd that the larger angular momentum quantum numbers l are, the smaller the corresponding maximum values of partial absorption cross section are. When themagnetic monopole charge βincreases, the absorption cross section and the power emission spectra of Hawking radiation increase, but the absorption probability and the luminosity decrease.In Chapter 5,we analyze the Schr¨odinger-type scalar wave equation and compute transmission coe?cients for arbitrary coupling of the ?eld to the background geometry with the WKB approximation. We numerically investigate its absorption cross section and analyze them in the high frequency regime. We ?nd that the absorption cross section oscillates about the geometric optical value and the limit of absorption cross section is uniform in the high frequency regime.In Chapter 6,we consider corrections to all orders in the Planck length on the quantum state density, and calculate the statistical entropy of the scalar ?eld on the background of the Bardeen regular black hole numerically. We obtain the distribution of entropy which is inside the horizon of black hole and the contribution of the vicinity of horizon taken great parts of the whole entropy.