Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics
Absztrakt:
In this paper we describe in full details a new family of
recently
found exact solutions of relativistic, perfect fluid dynamics.
With an
ansatz that generalizes the well-known Hwa-Bjorken solution we
obtain a
wide class of new exact, explicit, and simple solutions, which
have a
remarkable advantage as compared to presently known exact and
explicit
solutions: they do not lack acceleration. They can be utilized
for the
description of the evolution of the matter created in high
energy heavy
ion collisions. Because these solutions are accelerating, they
provide
a more realistic picture than the well-known Hwa-Bjorken
solution, and
give more insight into the dynamics of the matter. We exploit
this by
giving an advanced simple estimation of the initial energy
density of
the produced matter in high energy collisions, which takes
acceleration
effects, i.e., the work done by the pressure, and the modified
change
of the volume elements, into account. We also give an advanced
estimation of the life-time of the reaction. Our new solutions
can also
be used to test numerical hydrodynamical codes reliably. In the
end, we
also give an exact, 1+1 dimensional, relativistic hydrodynamical
solution, where the initial pressure and velocity profile is
arbitrary,
and we show that this general solution is stable for
perturbations.