Maximally Symmetric Boost-Invariant Solutions of the Boltzmann Equation in Foliated Geometries

TL;DR

This paper derives a unified, exact boost-invariant solution to the relativistic Boltzmann equation on a maximally symmetric background, generalizing known flows and introducing a new analytic solution called Grozdanov flow.

Contribution

It provides a symmetry-based, exact solution to the Boltzmann equation applicable to various constant-curvature foliations of $dS_3$, including a new hyperbolic foliation solution.

Findings

Reproduces Bjorken and Gubser flows as special cases.

Introduces a new analytic solution called Grozdanov flow.

Shows hydrodynamics and free streaming as limiting regimes.

Abstract

In this work we study the relativistic kinetic theory of a boost-invariant conformal gas on a static, maximally symmetric background $dS_3\times \mathbb{R}$, considering all constant-curvature slicings of $dS_3$ - flat, spherical, or hyperbolic- and their associated symmetry groups. Using a symmetry-driven cotangent-bundle approach, we show that the isometry group of each slicing acts on phase space in such a way that only its Casimir invariants and the time-like coordinate unconstrained, so the distribution function depends solely on these quantities. This yields a unified boost-invariant exact solution of the Boltzmann equation valid for each constant-curvature foliation of $dS_3\times \mathbb{R}$. Specializing this general solution to the flat and spherical foliations reproduces the Bjorken and Gubser flows, respectively, while its restriction to the hyperbolic foliation produces a genuinely new analytic solution (`Grozdanov flow'). Hydrodynamics and free streaming emerge naturally as limiting regimes of this novel exact solution. We further comment on several relevant aspects of the new boost-invariant solution on the hyperbolic slicing and on their interpretation once mapped back to Minkowski space.