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- W1995219312 abstract "We discuss hairy black hole solutions with scalar hair of scaling dimension $ensuremath{Delta}$ and (small) electromagnetic coupling ${q}^{2}$, near extremality. Using trial functions, we show that hair forms below a critical temperature ${T}_{c}$ in the region of parameter space $(ensuremath{Delta},{q}^{2})$ above a critical line ${q}_{c}^{2}(ensuremath{Delta})$. For $ensuremath{Delta}>{ensuremath{Delta}}_{0}$, the critical coupling ${q}_{c}^{2}$ is determined by the ${mathrm{AdS}}_{2}$ geometry of the horizon. For $ensuremath{Delta}<{ensuremath{Delta}}_{0}$, ${q}_{c}^{2}$ is below the value suggested by the near horizon geometry at extremality. We provide an analytic estimate of ${ensuremath{Delta}}_{0}$ (numerically, ${ensuremath{Delta}}_{0}ensuremath{approx}0.64$). We also compute analytically the true critical line for the entire range of the scaling dimension. In particular for $q=0$, we obtain an instability down to the unitarity bound. We perform explicit analytic calculations of ${T}_{c}$, the condensate and the conductivity. We show that the energy gap in units of ${T}_{c}$ diverges as we approach the critical line (${T}_{c}ensuremath{rightarrow}0$)." @default.
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- W1995219312 date "2012-07-03" @default.
- W1995219312 modified "2023-10-16" @default.
- W1995219312 title "Hair on near-extremal Reissner-Nordström AdS black holes" @default.
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- W1995219312 doi "https://doi.org/10.1103/physrevd.86.025002" @default.
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