# An exact solution for the relativistic dynamics of a strongly coupled plasma

**CAPTION**: Visualizations of the Minkowski-space evolution of the effective temperature obtained from the new exact solution to the Boltzmann equation. The top panels show the xy-plane (z = 0) and the bottom panels show the xz-plane (y = 0). The panels going from left to right correspond to three snapshots of the system's evolution.

### A new exact solution of the relativistic Boltzmann equation

Kent State University physics professor Dr. Michael Strickland and collaborators from McGill, Ohio State, and Sao Paulo Universities have discovered a new exact solution of the relativistic Boltzmann equation. Very few such exact solutions are known. The new exact solution discovered by Dr. Strickland and his collaborators is the first to describe a system that is expanding at relativistic velocities radially and longitudinally. This mimics the anisotropic expansion of the quark-gluon plasma created in relativistic heavy-ion collisions at the Large Hadron Collider at CERN. The exact solution made use of an ingenious mapping of Minkowski space onto a (3+1)-dimensional curved de Sitter geometry which was first applied to relativistic hydrodynamics by string theorist Steve Gubser (Princeton University). Using this method, Dr. Strickland and collaborators were able to map the solution of the (3+1)-dimensional Boltzmann equation to a one-dimensional problem that could be solved exactly. The new exact solution can be used to test relativistic viscous hydrodynamics models which describe quark-gluon plasma evolution macroscopically instead of microscopically. Having an exact solution to compare approximations with is important, since viscous hydrodynamic modeling is now a key component of any quantitative theoretical description of relativistic heavy-ion collisions. The method also has some promise for improving our understanding of astrophysical shocks, since shock simulations also heavily rely on relativistic hydrodynamics and kinetic theory. The reported work is available free from arXiv.org and has been published in Physical Review Letters as an "Editors' Suggestion".