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In this paper we describe in full details a new family of recently foundexact solutions of relativistic, perfect fluid dynamics. With an ansatz, whichgeneralizes the well-known Hwa-Bjorken solution, we obtain a wide class of newexact, explicit and simple solutions, which have a remarkable advantage ascompared to presently known exact and explicit solutions: they do not lackacceleration. They can be utilized for the description of the evolution of thematter created in high energy heavy ion collisions. Because these solutions areaccelerating, they provide a more realistic picture than the well-knownHwa-Bjorken solution, and give more insight into the dynamics of the matter. Weexploit this by giving an advanced simple estimation of the initial energydensity of the produced matter in high energy collisions, which takesacceleration effects (i.e. the work done by the pressure and the modifiedchange of the volume elements) into account. We also give an advancedestimation of the life-time of the reaction. Our new solutions can also be usedto test numerical hydrodynamical codes reliably. In the end, we also give anexact, 1+1 dimensional, relativistic hydrodynamical solution, where the initialpressure and velocity profile is arbitrary, and we show that this generalsolution is stable for perturbations.

Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics