Yves Brihaye

Holographic Superconductors in 3+1 dimensions away from the probe limit

We study holographic superconductors in 3+1 dimensions away from the probe limit, i.e. taking backreaction of the space-time into account. We consider the case of pure Einstein and Gauss-Bonnet gravity, respectively. Similar to the probe limit we observe that the critical temperature at which condensation sets in decreases with increasing Gauss-Bonnet coupling. The decrease is however stronger when taking backreaction of the space-time into account. We observe that the critical temperature becomes very small, but stays positive for all values of the Gauss-Bonnet coupling no matter how strong the backreaction of the space-time is.

Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method

We propose to compute the action and global charges of the asymptotically anti-de Sitter solutions in Einstein-Gauss-Bonnet theory by adding boundary counterterms to the gravitational action. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d ≤ 9. We apply this tehnique for several different types of black objects. Apart from static and rotating black holes, we consider also Einstein-Gauss-Bonnet black string solutions with negative cosmological constant.

Myers–Perry black holes with scalar hair and a mass gap

Abstract We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einsteins gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass M, two equal angular momenta J 1 = J 2 ≡ J and a conserved Noether charge Q, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers–Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair [1] . Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

The electroweak sphaleron at physical mixing angle

Abstract The electroweak sphaleron, known previously only in the spherical approximation at vanishing mixing, angle, is constructed for the physical value of the mixing angle sin2 θw=0.23. It is symmetric under rotations around the z-axis and parity reflections. Its energy density and total energy differ little from those of the spherical sphaleron.

Five-dimensional rotating black holes in Einstein–Gauss–Bonnet theory

Abstract We present arguments for the existence of five-dimensional rotating black holes with equal magnitude angular momenta in Einstein–Gauss–Bonnet theory with negative cosmological constant. These solutions posses a regular horizon of spherical topology and approach asymptotically an anti-de Sitter spacetime background. We discuss the general properties of these solutions and, using an adapted counterterm prescription, we compute their entropy and conserved charges.

Holographic superfluid/fluid/insulator phase transitions in 2+1 dimensions

We study the breaking of an Abelian symmetry close to the horizon of a black string as well as close to the tip of a solitonic, cigar-shaped solution in (3+1)-dimensional Anti-de Sitter space-time. We use these solutions to describe holographic superfluids away from the probe limit, i.e. taking backreaction into account. We observe that up to four phases exist in this model representing the duals of black string solutions with and without scalar hair and solitonic, cigar-shaped solutions with and without scalar hair, respectively. We construct the full phase diagram that describes the phase transitions between fluids and superfluids, between insulators and superfluids as well as between insulators and fluids. In the probe limit the phase transition from fluids to black string superfluids changes from being second order to first order for sufficiently large values of the superfluid velocity and/or the angular momentum of the dual black string. We find that if we take backreaction into account phase transitions that are first order for weak backreaction become again second order for sufficiently strong backreaction. Moreover, we find a new type of insulator/superfluid phase transition for strong backreaction and vanishing superfluid velocity as well as a new type of fluid/superfluid phase transition that exists only for non-vanishing superfluid velocity.

Particle-like solutions to higher-order curvature Einstein–Yang–Mills systems in d dimensions

We consider the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss–Bonnet (GB)) interacting with the superposition of the first two members of the Yang–Mills (YM) hierarchy, in d dimensions. The YM fields are taken to be in the chiral representations of the gauge groups, (i) SO(±)(d), and (ii) SO(±)(d − 1), respectively, for (i) even d and (ii) odd d. Such systems can occur in the low energy effective action of string theory. Particle-like solutions in dimensions d = 6, 8, and d = 7, are constructed, respectively. Our results reveal qualitatively new properties featuring double-branch solutions with critical behaviour. In this preliminary study, we have restricted numerical study to one-node solutions.

On the stability of AdS black strings

Abstract We explore via linearized perturbation theory the Gregory–Laflamme instability of the black string solutions of Einsteins equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and S d − 3 × S 1 are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser–Mitra conjecture.

Inside black holes with synchronized hair

Recently, various examples of asymptotically flat, rotating black holes (BHs) with synchronized hair have been explicitly constructed, including Kerr BHs with scalar or Proca hair, and Myers–Perry BHs with scalar hair and a mass gap, showing there is a general mechanism at work. All these solutions have been found numerically, integrating the fully non-linear field equations of motion from the event horizon outwards. Here, we address the spacetime geometry of these solutions inside the event horizon. Firstly, we provide arguments, within linear theory, that there is no regular inner horizon for these solutions. Then, we address this question fully non-linearly, using as a tractable model five dimensional, equal spinning, Myers–Perry hairy BHs. We find that, for non-extremal solutions: (1) the inside spacetime geometry in the vicinity of the event horizon is smooth and the equations of motion can be integrated inwards; (2) before an inner horizon is reached, the spacetime curvature grows (apparently) without bound. In all cases, our results suggest the absence of a smooth Cauchy horizon, beyond which the metric can be extended, for hairy BHs with synchronized hair.

Higher order curvature generalizations of Bartnick-McKinnon and coloured black hole solutions in d = 5

Abstract We construct globally regular as well as non-Abelian black hole solutions of a higher-order curvature Einstein–Yang–Mills (EYM) model in d =5 dimensions. This model consists of the superposition of the first two members of the gravitational hierarchy (Einstein plus first Gauss–Bonnet (GB)) interacting with the superposition of the first two members of the SO ( d ) Yang–Mills hierarchy.