Anisotropic plasma with a chemical potential and scheme-independent instabilities

Abstract

Generically, the black brane solution with planar horizons is thermodynamically stable. We find a counter-example to this statement by demonstrating that an anisotropic black brane is unstable. We present a charged black brane solution dual to a spatially anisotropic finite temperature N = 4 super Yang-Mills plasma at finite U(1) chemical potential. This static and regular solution is obtained both numerically and analytically. We uncover rich thermodynamic phase structures for this system by considering the cases when the anisotropy constant "a" takes real and imaginary values, respectively. In the case a(2) > 0, the phase structure of this anisotropic black brane is similar to that of Schwarzschild-AdS black hole with S-3 horizon topology, yielding a thermodynamical instability at smaller horizon radii. For the condition a(2) <= 0, the thermodynamics is dominated by the black brane phase for all temperatures. (C) 2014 The Authors. Published by Elsevier B.V.We are indebted to Hong Lu and Jian-Xin Lu for help on the Type IIB supergravity action. We would like also to thank LiQing Fang, Xiao-Mei Kuang, Jia-Rui Sun, Shang-Yu Wu, Yi Yang and Shao-Jun Zhang for helpful discussions. X.H.G. was supported by NSFC, China (No. 11375110), and Shanghai Rising-Star Program (No. 10QA1402300). S.J.S. was supported by the NRF, Korea (NRF-2013R1A2A2A05004846)