Mathematical Methods In The Research Of Black Holes

The idea of black hole appeared really early, while the research had not got any meaningful results until the beginning of the last century.It is because that the classical mechanics is based on the physical phenomenons of a macroscopic object moving slowly in a weak gravitation field.So we can not use it in the research of a test particle moving in a strong gravitation field at the research.In fact,people began to consider black holes in a scientific way after the Special Relativity and General Relativity appeared,and the system of mathematics had been build well enough to support them.We will start from the history of this research.In the first part of this article,we can see some important theories and results found in the past several decades,such as General Relativity,Vacuum Solutions,the theory of singularity,the four laws of black hole,etc.The focus of this part is Schwarzchild's vacuum solution and the four laws.We can how to build the models of black hole in a mathematical way.In the second part, we will introduce gravitomagnetism to the readers,including the background, the models,and an important object of this research --- cosmo jets. We will do some simple discussion on the gravitomagnetism jets by using the theories founded by B.Mashhoon.