Black holes with scalar hair and asymptotics in N = 8 supergravity

By T. Hertog, Kengo Maeda. 2004

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We consider = 8 gauged supergravity in D = 4 and D = 5. We show one can weaken the boundary conditions on the metric and on all scalars with m2 < − (D − 1)2/4 + 1 while preserving the asymptotic anti-de Sitter (AdS) symmetries. Each scalar admits a one-parameter family of AdS-invariant boundary conditions for which the metric falls off slower than usual. The generators of the asymptotic symmetries are finite, but generically acquire a contribution from the scalars. For a large class of boundary conditions we numerically find a one-parameter family of black holes with scalar hair. These solutions exist above a certain critical mass and are disconnected from the Schwarschild-AdS black hole, which is a solution for all boundary conditions. We show the Schwarschild-AdS black hole has larger entropy than a hairy black hole of the same mass. The hairy black holes lift to inhomogeneous black brane solutions in ten or eleven dimensions. We briefly discuss how generalized AdS-invariant boundary conditions can be incorporated in the AdS/CFT correspondence.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e42630eb29a371b97b622d96754978425af5c187

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Citations in the corpus

Comparison between various notions of conserved charges in asymptotically AdS spacetimes (2005, methodology): “When W(α) ∝ α3, however, G is larger and corresponds to the conformal isometry group of the Einstein static universe, G ∼= O(3, 2) [3, 12].”
Multi-trace deformations in AdS/CFT: exploring the vacuum structure of the deformed CFT (2007, background): “Requiring that this e ective action exists and is bounded from below reproduces recent results on the stability ofthe AdS vacuum in the presence of‘m ixed’boundary conditions. e-m ail:ioannis.papadimitriou@desy.de”
Exact black hole solution with a minimally coupled scalar field (2004, background): “The variation of the boundary term at the horizon, is obtained using δR|r+ = δR(r+)− R ′ ∣ ∣ r+ δr+ , δf2 ∣ ∣ r+ = − (f2)′ ∣ ∣ r+ δr+ , together with (3.4), in Eqs.”
AdS dyonic black hole and its thermodynamics (2013, background): “The third is where φ2 = cφ 2 1 [37] (see also [38].”
Gauge/String Duality, Hot QCD and Heavy Ion Collisions (2011, background): “It was later realized [320, 321] that even more general quantizations are possible in which the modes used to build the physical states have both A and B nonzero, with a relation between the two that ensures that the asymptotic symmetries of AdS are preserved [322,323].”
Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields (2006, background): “(2.1) For matter-free gravity, the asymptotic behavior of the metric is given in [14, 15, 16] and reads hrr = O(r −D−1) , hrm = O(r −D) , hmn = O(r −D+3).”
Phase transitions near black hole horizons (2005, background): “Subsequent developments of hairy anti-de Sitter black holes are summarized in [27, 28, 29, 30, 31].”
Holographic description of AdS cosmologies (2005, methodology): “As described in [17], the AdS invariant boundary conditions βk = −kα2 correspond instead to adding a triple trace term to the action S = S0 − k 3 ∫”
Towards a Big Crunch Dual (2004, background): “On the other hand, the mass of static, spherical black holes that are solutions with the same boundary conditions is positive [6].”