Random Motion Of Light Particles Near The Event Horizon In Schwarzschild Space-Time

Black holes are perhaps the most important objects in General Relativity,and the recent publication of the first images of black holes has further boosted the interest in such astrophysical objects.In Schwarzschild spacetime,light cannot reach the event horizon in finite time,which means that the interior of black hole is invisible to observers outside the event horizon.However,if black holes do exist,their interiors should be detectable,a goal that has kept scientists on the hunt for nearly a century,and the fact that black hole event horizons are still being debated in theoretical physics is evidence of their significance.The inability of light signals to cross the event horizon is a consideration in classical theory,which does not involve quantum fluctuations.However,in Stochastic Gravity theory,stress-energy fluctuations in the matter field will cause space-time near the event horizon to fluctuate,which means that the test particles will be perturbed and make random motion.Therefore,we study the motion of light particles near the Schwarzschild space-time horizon affected by stochastic perturbations.This study could serve as a attempt to investigate the possible quantum effects of black hole space-time on the motion of matter in their surroundings as well as the role of stochastic noise in destroying event horizons.The thesis divides into three parts.In the first part,we introduce the relevant preparatory knowledge.In the second part,we describe the main work and achievements of Stochastic Gravity theory.In the last part,based on the inspiration of Stochastic gravity,we abstract the influence of space-time fluctuation on light particles as stochastic noise,and construct two types of random motion equations of light particles in Schwarzschild space-time by stochastic differential equations.By numerically simulating the sample orbits and analyzing the properties of the probability density function based on Fokker-Planck equation to quantitatively characterize the effect of noise,we conclude that the probability of light particles reaching the event horizon in finite time is zero after considering the stochastic perturbation,which indicates that the stochastic perturbation can preserve the stability of the event horizon.