E. O. Pozdeeva

The quark-gluon plasma formed as a result of heavy-ion collisions is currently investigated actively both theoretically and experimentally. According to the holographic approach, forming a quark-gluon plasma in the four-dimensional world is associated with creating black holes in a five-dimensional anti-de Sitter space. The multiplicity of particles produced in heavy-ion collisions is then determined by the entropy of the five-dimensional black hole, which is estimated by the area of the trapped surface. To fit the experimental data for multiplicity Kiritsis and Taliotis have proposed to consider black holes formation in modified ${AdS}_5$ spaces with different $b$-factors. In this paper we consider the formation of black holes under collision of membranes in modified ${AdS}_5$ spaces with $b$-factors. Following the previous proposals we consider the power-law and exponential $b$-factors, as well as mixed types of $b$-factors. We study dynamics of the change of the trapped surface area depending on the energy for each investigated space. We find that the power-law and mixed factors fit better to the experimental date.

The phase diagram of quark gluon plasma (QGP) formed at a very early stage just after the heavy ion collision is obtained by using a holographic dual model for the heavy ion collision. In this dual model colliding ions are described by the charged shock gravitational waves. Points on the phase diagram correspond to the QGP or hadronic matter with given temperatures and chemical potentials. The phase of QGP in dual terms is related to the case when the collision of shock waves leads to formation of trapped surface. Hadronic matter and other confined states correspond to the absence of trapped surface after collision. Multiplicity of the ion collision process is estimated in the dual language as area of the trapped surface. We show that a non-zero chemical potential reduces the multiplicity. To plot the phase diagram we use two different dual models of colliding ions, the point and the wall shock waves, and find qualitative agreement of the results.