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The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution ofself-gravitating matter experiencing collisions with a fixed background ofparticles in the framework of a relativistic scalar theory of gravitation. Westudy the spatially-homogeneous system and prove global existence anduniqueness of solutions for the corresponding initial value problem in threemomentum dimensions. Additionally, we study the long time asymptotic behaviorof the system and prove that even in the absence of friction, solutions possessa non-trivial asymptotic profile. An exact formula for the long time limit ofthe particle density is derived in the ultra-relativistic case.

Spatially homogeneous solutions of the Vlasov-Nordstr\"om-Fokker-Planck system