Analytic solutions of the relativistic Boltzmann equation

Abstract

We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second order hydrodynamics and fluid-gravity correspondence.

arXiv comment18 pages.v3: update to match the published version

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Cited by in corpus (12)

• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Analytic solution of the Boltzmann equation in an expanding system
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Azimuthal Anisotropies at High Momentum from Purely Non-Hydrodynamic Transport
• A hydrodynamic approach to boost invariant free streaming
• Equilibration and freeze-out of an expanding gas in a transport approach in a Friedmann-Robertson-Walker metric
• Boltzmann-Langevin Approach to Pre-equilibrium Correlations in Nuclear Collisions
• Investigating the domain of validity of the Gubser solution to the Boltzmann equation
• Analytic approaches to relativistic hydrodynamics
• Kinetic evolution and correlation of fluctuations in an expanding quark gluon plasma
• Analytical Solution of the Nonlinear Relativistic Boltzmann Equation
• Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries