Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics

This thesis investigates the jet-medium interactions in a Quark-Gluon Plasma using a hydrodynamical model. It deals with the creation of Mach cones which are supposed to exhibit a characteristic structure in the measured angular particle distributions allowing for direct conclusions about the Equation of State and in particular about the speed of sound of the medium. Several different scenarios of jet energy loss are examined and different mechanisms of energy and momentum loss are analyzed, ranging from weak interactions (based on calculations from perturbative Quantum Chromodynamics, pQCD) to strong interactions (formulated using the Anti-de-Sitter/Conformal Field Theory Correspondence, AdS/CFT). Though they result in different angular particle correlations which could in principle allow to distinguish the underlying processes, it is shown that the characteristic structure observed in experimental data can be obtained due to the different contributions of several possible jet trajectories through an expanding medium. Such a structure cannot directly be connected to the Equation of State. In this context, the impact of a strong flow created behind the jet (the diffusion wake) is examined which is common to almost all jet deposition scenarios. Besides that, the transport equations for dissipative hydrodynamics are discussed which are fundamental for any numerical computation of viscous effects in a Quark-Gluon Plasma