The Lifespan Of Schwarzschild-de-Sitter Black Hole

As early as 200 years ago the British R.J.Michell and French P.S.Laplace had predicted the existence of "black hole" in the frame of Newtonian mechanics and particle theory of light, but Young’s double-slit interference experiment made the theory of dark star lose its support.In 1915, Albert Einstein proposed the general relativity, so that the black hole theory got rapid progress. But even that, people always think that black hole is a object not outward radiation energy. Until 1974, since Hawking theoretically demonstrated that black holes are with thermal radiation, people are keen on calculating the lifespan and Speculated the evolution process of the black hole. And the ultimate fate of Hawking radiation, correction of uncertainty relation in quantum theory, etc., has always been the important topic to theoretical physicists.On the basis of existing research, this paper will use the corrected Stefan-Boltzmann law to calculate the lifespan of Schwarzschild de-Sitter black hole.The results are consistent with previous work.In this paper, we will correct the Stefan-Boltzmann law in the frame of GUP.We find that the corrected Stefan-Boltzmann law contains two terms, the4 T term and the6 T term. The coefficient of4 T is no longer constant which relates to the parameter of thin film model and the event horizon distance. While the6 T correction term results in an even more interesting phenomenon that a black hole will arrived limited highest temperature and leave a residual mass in the end of its lifespan. It is noted that the mass of the residue and the Planck mass are in the same order of magnitude.After the analysis in the paper, we found that the correction of lifespan is very small. But it still has its significance, because it will be reference value for the research of Hawking radiation and the quantization of gravity.Another purpose of this paper is that using the Schwarzschild-de-Sitter black hole to check the reliability of the observe and the theoretical values of the cosmological constant respectively, and results show that the observed value is more reliable.The paper is divided into three chapters:First chapter is the introduction part, including the research history of the black hole and the research object Schwarzschild-de-Sitter black hole, the mechanism of Hawking radiation and the Stefan-Boltzmann law, how to calculate the lifespan of Schwarzschild black hole, and generalized uncertainty principle.The second chapter is about calculation, including the calculation of the radiant flux density in the frame of the generalized uncertainty principle, then get the corrected Stefan-Boltzmann law, solution to the high temperature and the discussion of the cosmological constant and residual mass, finally get the lifespan of a Schwarzschild-de-Sitter black hole.The last chapter is conclusion, including the analysis of calculation results,references, and the summary and Prospect of the work.