Abstract
We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in mathcal{N} = 4 Chern-Simons AdS5 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.
Highlights
Chern-Simons (CS) supergravity [1] provides an excellent theoretical laboratory to investigate many theoretical aspects of gravitational physics, including black holes
We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in N = 4 Chern-Simons AdS5 supergravity
Contrary to the Ξ-neutral case found in Subection 4.1 which is pure gauge, and where the BPS equation is solved by the vacuum state in section 5.3, here we find a non trivial solution to the BPS equation, corresponding to the extremal black hole condition μ = 1, where the axial torsion charge C remains completely arbitrary, up to topological considerations that will be discussed in subsection 6.1
Summary
Chern-Simons (CS) supergravity [1] provides an excellent theoretical laboratory to investigate many theoretical aspects of gravitational physics, including black holes. In spite of containing quadratic-curvature terms in the gravitational part of the action, the field equations of the theory are of second order, which follows from the fact that CS gravity is a particular case of Lovelock theory. This makes the theory free of ghosts and tractable analytically. Many sectors of the solution space of the CS (super-)gravity theory can be explicitly worked out This includes black holes [7,8,9,10], wormholes [11], geometries with anisotropic scale invariance [12, 13], pp-waves, and many other interesting geometries [14]. The existence of such a diversity in the configuration space is somehow associated to certain degree of degeneracy that the theory exhibits, which relates to its peculiar dynamical structure [15, 16]
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