Jet quenching and holographic thermalization with a chemical potential

We investigate jet quenching of virtual gluons and thermalization of a strongly-coupled plasma with a non-zero chemical potential via the gauge/gravity duality. By tracking a charged shell falling in an asymptotic AdS d +1 background for d = 3 and d = 4, which is characterized by the AdS-Reissner-Nordström-Vaidya (AdS-RN-Vaidya) geometry, we extract a thermalization time of the medium with a non-zero chemical potential. In addition, we study the falling string as the holographic dual of a virtual gluon in the AdS-RN-Vaidya spacetime. The stopping distance of the massless particle representing the tip of the falling string in such a spacetime could reveal the jet quenching of an energetic light probe traversing the medium in the presence of a chemical potential. We find that the stopping distance decreases when the chemical potential is increased in both AdS-RN and AdS-RN-Vaidya spacetimes, which correspond to the thermalized and thermalizing media respectively. Moreover, we find that the soft gluon with an energy comparable to the thermalization temperature and chemical potential in the medium travels further in the non-equilibrium plasma. The thermalization time obtained here by tracking a falling charged shell does not exhibit, generically, the same qualitative features as the one obtained studying non-local observables. This indicates that — holographically — the definition of thermalization time is observer dependent and there is no unambiguos definition