Sound waves and solitons in hot and dense nuclear matter

TL;DR

This paper investigates the propagation of sound waves and solitons in hot, dense nuclear matter modeled as a relativistic fluid, revealing conditions for soliton formation, damping effects, and shock wave behavior.

Contribution

It introduces a relativistic hydrodynamic model based on a non-linear Walecka model to analyze density perturbations and soliton solutions in nuclear matter at finite temperature.

Findings

Single soliton solutions identified in linear perturbations

Damping effects depend on the equation of state

Spherical perturbations are strongly damped

Abstract

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density fluctuations. We solve them numerically for linear and spherical perturbations and follow the time evolution of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by radiation. Depending on the equation of state a strong damping may occur. Spherical perturbations are strongly damped and almost do not propagate. We study these equations also for matter at finite temperature. Finally we consider the limiting case of shock wave formation.