Femtoscopy is a unique tool to investigate the space-time geometry of the matter created in ultra-relativistic collisions. If the probability density distribution of hadron emission is parametrized, then the dependence of its parameters on particle momentum, collision energy, and collision geometry can be given. In recent years, several measurements came to light that indicated the adequacy of assuming a Lévy-stable shape for the mentioned distribution. In parallel, several new phenomenological developments appeared, aiding the interpretation of the experimental results, or providing tools for the measurements. In this paper we review and discuss some of these advances, phenomenological and experimental.

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail.

We utilize known exact analytic solutions of perfect fluid hydrodynamics to analytically calculate the polarization of baryons produced in heavy ion collisions. Assuming local thermodynamical equilibrium also for spin degrees of freedom, baryons get a net polarization at their formation (freeze-out). This polarization depends on the time evolution of the Quark-Gluon Plasma (QGP), which can be described as an almost perfect fluid. By using exact analytic solutions, we thus can analyze the necessity of rotation (and vorticity) for non-zero net polarization. In this paper we give the first analytical calculations for the polarization four-vector. We use two hydrodynamical solutions; one is the spherically symmetric Hubble flow (a somewhat oversimplified model, to demonstrate the methodology). The other solution which we use is a somewhat more involved one that corresponds to a rotating and accelerating expansion, and is thus well suited to investigate some main features of the time evolution of the QGP created in peripheral heavy-ion collisions (although there are still many numerous features of a real collision geometry that are beyond the reach of this simple model). Finally we illustrate and discuss our results on the polarization.