Article

# Small hairy black holes in AdS 5 × S 5

(Impact Factor: 6.11). 11/2011; 11(11). DOI: 10.1007/JHEP11(2011)035
Source: arXiv

ABSTRACT

We study small hairy black holes in a consistent truncation of $$\mathcal{N}$$ = 8 gauged supergravity that consists of a single charged scalar field interacting with the metric and a U(1) gauge field. Small very near extremal RNAdS black holes in this system are unstable to decay by superradiant emission. The end point of this instability is a small hairy black hole that we construct analytically in a perturbative expansion in its charge. Unlike their RNAdS counterparts, hairy black hole solutions exist all the way down to the BPS bound, demonstrating that $$\mathcal{N}$$ = 4 Yang Mills theory has an $$\mathcal{O}$$(N
2) entropy at all energies above supersymmetry. At the BPS bound these black holes reduce to previously discussed regular, supersymmetric horizon free solitons. We use numerical methods to continue the construction of these solitons to large charges and find that the line of soliton solutions terminates at a singular solution S at a finite charge. We conjecture that a one parameter family of singular supersymmetric solutions, which emerges out of S, constitutes the BPS limit of hairy black holes at larger values of the charge. We analytically determine the near singularity behaviour of S, demonstrate that both the regular and singular solutions exhibit an infinite set of damped ‘self similar’ oscillations around S and analytically compute the frequency of these oscillations. At leading order in their charge, the thermodynamics of the small hairy black holes constructed in this paper turns out to be correctly reproduced by modeling these objects as a non interacting mix of an RNAdS black hole and the supersymmetric soliton in thermal equilibrium. Assuming that a similar non interacting model continues to apply upon turning on angular momentum, we also predict a rich family of rotating hairy black holes, including new hairy supersymmetric black holes. This analysis suggests interesting structure for the space of (yet to be constructed) hairy charged rotating black holes in AdS
5 × S
5, particularly in the near BPS limit.

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Available from: Shiraz Minwalla
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• "Recently there has been a great interest in studying black holes with a condensate of some field outside the horizon [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] 1 . Often there is also a black hole with the same charges as the black hole with a condensate outside but with a lower Bekenstein Hawking entropy. "
##### Article: Black rings with fourth dipole cause less hair loss
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ABSTRACT: An example of entropy enigma with a controlled CFT dual was recently studied in arXiv:1108.0411. The enigmatic bulk configurations, considered within the STU model, can be mapped under spectral flow into black rings with three monopole and dipole charges. Even though the bulk and CFT configurations existed in the same region of parameter space, the Bekenstein-Hawking entropy of the bulk configurations was found to be lower than the microscopic entropy from the CFT. While it is possible that the difference in entropy is due to the bulk and boundary configurations being at different points in the moduli space, it is also possible that the bulk configurations embeddable within the STU model are not the most entropic. New families of BPS black ring solutions with four electric and four dipole magnetic charges have recently been explicitly constructed in arXiv:1201.2585. These black rings are not embeddable within the STU model. In this paper we investigate if these black rings can be entropically dominant over the STU model black rings. We find that the new black rings are always entropically subdominant to the STU-model black rings. However, for small fourth dipole charge these black rings continue to be dominant over the BMPV in a small region of parameters and are thus enigmatic.
Full-text · Article · Apr 2012 · Journal of High Energy Physics
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• "For example, [1] [2] [3] [4] [5] [6] found that a Reissner–Nordstrom black brane in AdS Maxwell gravity with a charged scalar (in bottom-up settings or embedded in string theory) is unstable against forming a charged scalar condensate outside its horizon and breaking the U(1) symmetry, and related this to the superconducting phase transition in the boundary field theory. As a different example embeddable in string theory, [7] studied a small R-charged black hole in AdS 5 × S 5 . They found that the black hole is unstable against forming an R-charged scalar condensate around it and constructed the endpoint configuration perturbatively when the charge is small. "
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Full-text · Article · Aug 2011 · Journal of High Energy Physics
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##### Article: Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion
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ABSTRACT: In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it. Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHEP
Preview · Article · May 2010 · Journal of High Energy Physics