Energy loss at zero temperature from extremal black holes

Abstract

Using the AdS/CFT correspondence, we probe the extremal black holes by studying the energy loss of a moving heavy point particle in a strongly-coupled boundary field theory at zero temperature and finite charge density. We first consider the extremal AdS-Reissner-Nordström (AdSRN) background black hole in the bulk and find an analytic solution of drag force which depends on the finite charge density of the boundary field theory. By studying the near horizon geometry of trailing string in the bulk, one finds the IR divergency does not show the logarithmic behavior. This result would be a general property of extremal backgrounds. We also extend our study to the extremal backgrounds with vanishing entropy density in appropriate extremal limits. After studying the Langevin coefficients, it is shown that in the extremal black hole backgrounds the longitudinal Langevin diffusion coefficient along the semiclassical string motion is larger compared to that of the transverse direction.