P. Meessen
We discus all possible spherically symmetric black hole type solutions to an N=2 supergravity model with SO(3) gauging. The solutions consist of a one parameter family illustrating that the no-hair theorem does not hold and an isolated solution that a supersymmetric analogue of a coloured black hole.
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Hairy black holes (BHs) have macroscopic degrees of freedom which are not associated with a Gauss law. As such, these degrees of freedom are not manifest as quasi-local quantities computed at the horizon. This suggests conceiving hairy BHs as an interacting system with two components: a "bald" horizon coupled to a "hairy" environment. Based on this idea we suggest an effective model for hairy BHs -- typically described by numerical solutions -- that allows computing analytically thermodynamic and other quantities of the hairy BH in terms of a fiducial bald BH. The effective model is universal …
It has been shown recently that there is a large class of supersymmetric solutions of five-dimensional supergravity which generalize the supersymmetric black ring solution of Elvang et al. This class involves arbitrary functions. We show that most of these solutions do not have smooth event horizons, so they do not provide examples of black objects with infinite amounts of "hair".
We construct a new class of charged, rotating hairy black holes in a consistent truncation of $\mathcal{N} = 8$ supergravity, which retains one charged scalar field and a U$(1)$ gauge field. These hairy solutions can be uplifted to solutions of type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. We find rotating hairy black holes with finite entropy arbitrarily close to the supersymmetric bound - the resulting supersymmetric solution is a one-parameter extension of the Gutowski-Reall solution. These solutions have finite curvature invariants (including at extremality), but in the extrem…
We present a numerical study of fully non-linear, rotating and charged hairy black hole solutions in five-dimensional anti-de Sitter space, which originate from a consistent truncation of $\mathcal{N}=8$ supergravity, and can be consistently embedded in type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. The hairy black holes have one scalar field charged under a $U(1)$ gauge field, and branch from the near-extremal Cvetič, Lü and Pope solutions. We give numerical evidence that the hairy solutions exist arbitrarily close to the BPS bound for all charges, and saturate it in the $T\righta…
We study small hairy black holes in a consistent truncation of ${\cal N}=8$ 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 ${\cal N}=4$ Yang Mills theory has an ${\ca…
We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically…
In this article we study a family of four-dimensional, $\mathcal{N}=2$ supergravity theories that interpolates between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\mathcal{N}=8$ supergravity. In this infinitely many theories characterized by two real numbers -- the interpolation parameter and the dyonic "angle" of the gauging -- we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supers…
We consider the linear stability of $4$-dimensional hairy black holes with mixed boundary conditions in Anti-de Sitter spacetime. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged $\mathcal{N}=8$ supergravity in four dimensions, $m^{2}=-2l^{-2}$. It is shown that the Schrödinger operator on the half-line, governing the $S^{2}$, $H^{2}$ or $\mathbb{R}^{2}$ invariant mode around the hairy black hole, allows for non-trivial self-adjoint extensions and each of them correspons to a class of mixed boundary conditions in the gravitational theory. Discardin…
This is a short review of classical solutions with gravitating Yang-Mills fields in $D>4$ spacetime dimensions. The simplest SO(4) symmetric particlelike and SO(3) symmetric vortex type solutions in the Einstein-Yang-Mills theory in D=5 are considered, and their various generalizations with or without an event horizon, for other symmetries, in more general theories, and also in $D>5$ are described. In addition, supersymmetric solutions with gravitating Yang-Mills fields in string theory are discussed.
We construct analytical supersymmetric coloured black hole solutions, i.e. non-Abelian black hole solutions that have no asymptotic non-Abelian charge but do have non-Abelian charges on the horizon that contribute to the Bekenstein-Hawking entropy, to two SU(3)-gauged N=2 d= supergravities. The analytical construction is made possible due to the fact that the main ingredient is the Bogomol'nyi equation, which under the assumption of spherical symmetry admits a Lax pair formulation. The Lax matrix needed for the coloured black holes must be defective which, even though it is the non-generic and…
We find broad classes of exact 4-dimensional asymptotically flat black hole solutions in Einstein-Maxwell theories with a non-minimally coupled dilaton and its non-trivial potential. We consider a few interesting limits, in particular, a regular generalization of the dilatonic Reissner-Nordstr{ö}m solution and, also, smooth deformations of supersymmetric black holes. Further examples are provided for more general dilaton potentials. We discuss the thermodynamical properties and show that the first law is satisfied. In the non-extremal case the entropy depends, as expected, on the asymptotic va…
In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\,\mathcal{N}=2$ supergravity theories interpolating between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\,\mathcal{N}=8$ supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable ch…
We construct black holes with scalar hair in a wide class of four-dimensional N=2 Fayet-Iliopoulos gauged supergravity theories that are characterized by a prepotential containing one free parameter. Considering the truncated model in which only a single real scalar survives, the theory is reduced to an Einstein-scalar system with a potential, which admits at most two AdS critical points and is expressed in terms of a real superpotential. Our solution is static, admits maximally symmetric horizons, asymptotically tends to AdS space corresponding to an extremum of the superpotential, but is dis…
Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $…
We construct a supersymmetric black ring solution of SU(2) N=1, d=5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric coloured black holes recently constructed in th…
New phases of $\mathcal{N}=4$ SYM at finite chemical potential
本研究通过AdS$_5$/CFT$_4$对应关系系统搜索与有限化学势下$\n=4$ SYM热态对偶的超引力解，构造并分析了两类自洽截断中的静态带电毛状解，助力理解SYM热态全相空间。
By identifying a bosonic consistent truncation from the 1/4-BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory. Reductions of a large class of supersymmetric solutions corresponding to wrapped M2 and M5-branes lead to black strings and warped AdS3 solutions preserving supersymmetry. With a view to AdS/CMT applications, we also construct a numerical hairy BTZ black hole and, as a preliminary step in this direction, determine the conductivity of the dual CFT.
Large AdS black holes from QFT
本研究通过自由QFT分析和背景场方法推导大N下$\n=4$杨-米尔斯理论的指标，其饱和AdS$_5$黑洞的贝肯斯坦-霍金熵以解释微观态，还探究了Macdonald指标及AdS$_7$黑洞相关问题。
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