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Register a new userBlack holes with topological charges in Chern-Simons AdS$_5$ supergravity
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We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in $mathcal{N}=4$ Chern-Simons AdS$_5$ supergravity. They are governed by three parameters associated to the mass, axial torsion and amplitude of the internal soliton, and two ones to the gravitational hair. They describe geometries that can be a global AdS space, naked singularity or a (non-)extremal black hole. We analyze physical properties of two inequivalent asymptotically AdS solutions when the spatial section at radial infinity is either a 3-sphere or a projective 3-space. An important feature of these 3-parametric solutions is that they possess a topological structure including two $SU(2)$ solitons that wind nontrivially around the black hole horizon, as characterized by the Pontryagin index. In the extremal black hole limit, the solitons strengths match and a soliton-antisoliton system unwinds. That limit admits both non-BPS and BPS configurations. For the latter, the pure gauge and non-pure gauge solutions preserve $1/2$ and $1/16$ of the original supersymmetries, respectively. In a general case, we compute conserved charges in Hamiltonian formalism, finding many similarities with standard supergravity black holes.
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Based on recent discussions on the so-called unconventional supersymmetry, we propose a 5D Chern-Simons AdS-$mathcal{N}$-SUGRA formulation without gravitino fields and show that a residual local SUSY is preserved. We explore the properties of CS theories to find a solution to the field equations in a 5D manifold. With a Randall-Sundrum-type ansatz, we show that this particular dimensional reduction is compatible with SUSY, and some classes of 4D solutions are then analyzed.
We extend our recent work on the quasilocal formulation of conserved charges to a theory of gravity containing a gravitational Chern-Simons term. As an application of our formulation, we compute the off-shell potential and quasilocal conserved charges of some black holes in three-dimensional topologically massive gravity. Our formulation for conserved charges reproduces very effectively the well-known expressions on conserved charges and the entropy expression of black holes in the topologically massive gravity.
We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of CS coupling constant beyond its supergravity amount, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and do not manifest uniquely by their global charges.
We construct dynamical black hole solutions with a helical symmetry in AdS$_5$, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is $Rtimes SU(2)$. This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers-Perry-AdS$_5$, where the black resonators emerge from the onset of a superradiant instability of the Myers-Perry-AdS$_5$ with equal angular momenta and are connected to the geons in the small horizon limit. The angular velocities of the black resonators always satisfy $Omega>1$ in units of the AdS radius. A black resonator is shown to have higher entropy than a Myers-Perry-AdS$_5$ black hole with the same asymptotic charges. This implies that the Myers-Perry-AdS$_5$ can dynamically evolve into the black resonator under the exact $SU(2)$-symmetry although its endpoint will be further unstable to $SU(2)$-violating perturbations.
In this paper, we analyze the static solutions for the $U(1)^{4}$ consistent truncation of the maximally supersymmetric gauged supergravity in four dimensions. Using a new parametrization of the known solutions it is shown that for fixed charges there exist three possible black hole configurations according to the pattern of symmetry breaking of the (scalars sector of the) Lagrangian. Namely a black hole without scalar fields, a black hole with a primary hair and a black hole with a secondary hair respectively. This is the first, exact, example of a black hole with a primary scalar hair, where both the black hole and the scalar fields are regular on and outside the horizon. The configurations with secondary and primary hair can be interpreted as a spontaneous symmetry breaking of discrete permutation and reflection symmetries of the action. It is shown that there exist a triple point in the thermodynamic phase space where the three solution coexist. The corresponding phase transitions are discussed and the free energies are written explicitly as function of the thermodynamic coordinates in the uncharged case. In the charged case the free energies of the primary hair and the hairless black hole are also given as functions of the thermodynamic coordinates.
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