Stability of black holes and solitons in Anti-de Sitter space-time

Hartmann, Betti

doi:10.1016/j.nuclphysbps.2014.04.008

Cited by 3 publications

(1 citation statement)

References 64 publications

(74 reference statements)

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“…For a charged scalar field coupled to Einstein-Maxwell theory a similar situation occurs: at small temperatures charged scalar hair forms and the resulting "hairy black holes" are thermodynamically preferred [90][91][92][93][94][95][96][97]. This means that in the presence of a charged scalar field, the left-most branch of small black holes in the Gibbs free diagram Figure 8, although locally thermodynamically stable, does not globally minimize the Gibbs free energy.…”

Section: Charged Ads Black Holementioning

confidence: 97%

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

et al. 2014

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In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential-the Gibbs free energy-and study its behavior to uncover possible thermodynamic phase transitions in these black hole spacetimes. We show that the multiply-rotating Kerr-AdS black holes exhibit a rich set of interesting thermodynamic phenomena analogous to the "every day thermodynamics" of simple substances, such as reentrant phase transitions of multicomponent liquids, multiple first-order solid/liquid/gas phase transitions, and liquid/gas phase transitions of the van der Waals type. Furthermore, the reentrant phase transitions also occur for multiply-spinning asymptotically flat Myers-Perry black holes. These phenomena do not require a variable cosmological constant, though they are more naturally understood in the context of the extended phase space. The thermodynamic volume, a quantity conjugate to the thermodynamic pressure, is studied for AdS black rings and demonstrated to satisfy the reverse isoperimetric inequality; this provides a first example of calculation confirming the Galaxies 2014, 2 90 validity of isoperimetric inequality conjecture for a black hole with non-spherical horizon topology. The equation of state P = P (V, T ) is studied for various black holes both numerically and analytically-in the ultraspinning and slow rotation regimes.

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Section: Charged Ads Black Holementioning

confidence: 97%

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

et al. 2014

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Hairy black holes: Stability under odd-parity perturbations and existence of slowly rotating solutions

2014

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We show that, independently of the scalar field potential and of specific asymptotic properties of the spacetime (asymptotically flat, de Sitter or anti-de Sitter), any static, spherically symmetric or planar, black hole solution of the Einstein theory minimally coupled to a real scalar field with a general potential is mode stable under linear odd-parity perturbations. To this end, we generalize the Regge-Wheeler equation for a generic self-interacting scalar field, and show that the potential of the relevant Schrödinger operator can be mapped, by the so-called S-deformation, to a semipositively defined potential. With these results at hand we study the existence of slowly rotating configurations. The frame dragging effect is compared with the corresponding effect in the case of a Kerr black hole.

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Magnetic field in holographic superconductor with dark matter sector

2015

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Based on the analytical technique the effect of the static magnetic field on the s-wave holographic superconductor with dark matter sector of U(1)-gauge field type coupled to the Maxwell field has been examined. In the probe limit, we obtained the mean value of the condensation operator. The nature of the condensate in an external magnetic field as well as the behaviour of the critical field close to the transition temperature has been revealed. The obtained upturn of the critical field curves as a function of temperature, both in four and five spacetime dimensions, is a fingerprint of the strong coupling approach.Comment: 13 pages, RevTex, 2 figures, to be published in Phys.Rev.D15. arXiv admin note: text overlap with arXiv:1411.079

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Stability of black holes and solitons in Anti-de Sitter space-time

Cited by 3 publications

References 64 publications

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume

Hairy black holes: Stability under odd-parity perturbations and existence of slowly rotating solutions

Magnetic field in holographic superconductor with dark matter sector

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