Distribution Of Hawking Radiation, Correction Of Physical Constant, Mach’s Principle Model, Field In Wormhole, And Duality Transform Method

This thesis consists of six parts:(1)the statistical distribution of Hawking radiation particles outside the black hole horizon;(2)a model of the origin of physical constants and their quantum correction;(3)the exact solution of Mach’s principle model;(4)the solution of scalar fields in traversable wormholes;(5)the energy condition and the geodesic equation in the Robertson-Walker metric and the proximal Schwarzschild metric;(6)an indirect approach for solving eigenproblems by duality transform.The Hawking radiation usually considers the solutions on the horizon.We give the statistical distribution of radiation particles outside the horizon.We use the ingoing Eddington–Finkelstein coordinate to calculate the exact solution.By the exact solution,we calculate the radiation temperature on the horizon,which agrees with Hawking’s result.Based on the exact solution,we calculate the statistical distribution of radiation particles outside the horizon.We suggest a scheme for calculating the quantum correction of the gravitational constant.In the model,the gravitational constant originates from a coupling between the gravitational field and a scalar field.When the scalar field is a quantum field,there will be a time-and space-dependent quantum correction of the gravitational constant.The order of magnitude of the quantum correction is at a quantum level.There is no generally accepted physical theory about the origin of physical constants.We build a field model and a mechanics model for the origin of mass and the coupling constant.In the model,the mass and the coupling constant originate from a coupling between the matter field and an unobservable field.We also calculate the quantum correction of mass and the coupling constant with this model.Mach’s Principle states that the mass of matter is determined by all matter in the universe.We construct a model for Mach’s principle and obtain some exact solutions.We find that there exists a black hole solution in a static spherically symmetric solution of the Mach’s principle model.Under the Robertson-Walker metric,the model gives a time-dependent Hubble constant and a time-dependent gravitational constant.The traversable wormhole violates the energy conditions.We discuss the property of traversable wormholes by solving the scalar field in a traversable wormhole spacetime.We find a general behavior of the asymptotic solution of scalar fields in the wormhole throat and at infinity.Hawking and Penrose suggest that one can use the energy conditions to discuss singularities.We give the energy condition and the geodesic equation in the Robertson-Walker metric and the proximal Schwarzschild metric.We discuss the violation of the energy condition in traversable wormholes with the proximal Schwarzschild metric.An indirect method for solving eigenproblems by dual transform is proposed.The method first constructs the dual family of the potential that one wants to solve,then solves the most easily solved potential in the dual family,and then obtains the solution of the potential by dual transform.