Brownian motion around black hole

Brownian motion theory is always challenging to describe diffusion phenomena around a black hole, with the main issue is how to extend the classical theory of Brownian motion to the general relativity framework. In this study, we extended the Brownian motion theory in a curved space-time come from a strong gravitational field on the Schwarzschild black hole. The Brownian motion theory in Schwarzschild space-time was derived by using the Fokker-Planck equation, and the stationary solution was analyzed by Ito, Stratonovich-Fisk, and Hanggi-Klimontovich Approach. The numerical result was found that the Brownian motion in Schwarzschild space-time 1 was reduced to the standard Brownian motion in Newtonian classical theory. According to the Hanggi-Klimontovich approach for 1 the result showed a consistent with the relativistic Maxwell distribution. The Fokker-Planck equation in Schwarzschild space-time was also formulated as a generalization of relativistic Brownian motion theory. This work could open a promising interpretation to formulate the diffusion phenomena around a massive object in the general relativity framework