The Gubser solution of the relativistic Boltzmann equation and its domain of validity

In this work we study the evolution of the one particle phase space distribution which is an exact solution to the relativistic Boltzmann equation. This solution describes a conformal system undergoing Gubser flow in the de Sitter space times a line $dS_3\otimes R$. We show that depending on the initial condition the distribution function can become negative in certain kinematic regions of the available phase space. This non-physical behaviour of the distribution function restricts the validity of its applicability and imposes physical constraints on the initial conditions.