Energy loss at zero temperature from extremal black holes

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 Reissner-Nordstr$\rm\ddot{o}$m-AdS (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, we show the IR divergency does not show the logarithmic behavior. We study also the stochastic behavior of the probe and find the Langevin diffusion coefficients. This study is extended to the extremal backgrounds with vanishing entropy density in appropriate extremal limits.

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