Hair on near-extremal Reissner-Nordstrøm AdS black holes

Physics

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We discuss hairy black hole solutions with scalar hair of mass m and (small) electromagnetic coupling q^2, near extremality. Hair forms below a critical temperature Tc and for q^2 > qc^2 where qc^2 is determined by the AdS2 geometry of the horizon and can be negative. At the critical point q^2 = qc^2, the critical temperature vanishes; there is no instability below qc^2. We perform explicit analytic calculations of Tc, the condensate and the conductivity for m^2 =-2, in which case qc^2 = - 14. We show that the gap in units of Tc diverges as Tc->0. We find no discontinuity in the behavior of the system across q^2 = 0.

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