Relativistic Diffusion in G\"odel's Universe

K. G\"odel [G1] discovered his celebrated solution to Einstein equations in 1949. Additional contributions were made by Kundt [K] and Hawking-Ellis ([H-E],5.7). On the other hand, a general Lorentz invariant operator, associated to the so-called "relativistic diffusion'', and making sense in any Lorentz manifold, was introduced by Franchi-Le Jan in [F-LJ]. Here is purposed a first study of the relativistic diffusion in the framework of G\"odel's universe, which contains matter.