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Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2011). Gribov ambiguity in asymptotically AdS threedimensional gravity. Phys. Rev. D, 83(6), 7 pp.
Abstract: In this paper the zero modes of the de Donder gauge FaddeevPopov operator for threedimensional gravity with negative cosmological constant are analyzed. It is found that the AdS(3) vacuum produces (infinitely many) normalizable smooth zero modes of the FaddeevPopov operator. On the other hand, it is found that the BanadosTeitelboimZanelli black hole (including the zero mass black hole) does not generate zero modes. This differs from the usual Gribov problem in QCD where, close to the maximally symmetric vacuum, the FaddeevPopov determinant is positive definite while "far enough'' from the vacuum it can vanish. This suggests that the zero mass BanadosTeitelboimZanelli black hole could be a suitable ground state of threedimensional gravity with negative cosmological constant. Because of the kinematic origin of this result, it also applies for other covariant gravity theories in three dimensions with AdS(3) as maximally symmetric solution, such as new massive gravity and topologically massive gravity. The relevance of these results for supersymmetry breaking is pointed out.

Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2011). Black holes with gravitational hair in higher dimensions. Phys. Rev. D, 84(8), 10 pp.
Abstract: A new class of vacuum black holes for the most general gravity theory leading to second order field equations in the metric in even dimensions is presented. These spacetimes are locally antide Sitter in the asymptotic region, and are characterized by a continuous parameter that does not enter in the conserve charges, nor it can be reabsorbed by a coordinate transformation: it is therefore a purely gravitational hair. The black holes are constructed as a warped product of a twodimensional spacetime, which resembles the rt plane of the BanadosTeitelboimZanelli black hole, times a warp factor multiplying the metric of a D – 2dimensional Euclidean base manifold, which is restricted by a scalar equation. It is shown that all the Noether charges vanish. Furthermore, this is consistent with the Euclidean action approach: even though the black hole has a finite temperature, both the entropy and the mass vanish. Interesting examples of base manifolds are given in eight dimensions which are products of Thurston geometries, giving then a nontrivial topology to the black hole horizon. The possibility of introducing a torsional hair for these solutions is also discussed.

Anabalon, A., Canfora, F., Giacomini, A., & Oliva, J. (2012). Black holes with primary hair in gauged N=8 supergravity. J. High Energy Phys., (6), 12 pp.
Abstract: 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.
Keywords: Black Holes; Supergravity Models
