More on five dimensional EVH black rings

Abstract

In this paper we continue our analysis of arXiv:1308.1478 and study in detail the parameter space of three families of doubly spinning black ring solutions: balanced black ring, unbalanced ring and dipole-charged balanced black rings. In all these three families the Extremal Vanishing Horizon (EVH) ring appears in the vanishing limit of the dimensionful parameter of the solution which measures the ring size. We study the near horizon limit of the EVH black rings and for all three cases we find a (pinching orbifold) AdS 3 throat with the AdS 3 radius ℓ 2 = 8G 5 M/(3π) where M is the ring mass and G 5 is the 5d Newton constant. We also discuss the near horizon limit of near-EVH black rings and show that the AdS 3 factor is replaced with a generic BTZ black hole. We use these results to extend the EVH/CFT correspondence for black rings, a 2d CFT dual to near-EVH black rings.

On classification of geometries with SO(2,2) symmetry

“…Our interest in these geometries is primarily motivated by the fact that there is a special class of extremal black holes, Extremal Vanishing Horizon (EVH) black holes, where in the near horizon limit lead to such geometries, see [1,[9][10][11][12][13][14][15] for previous analysis of EVH black holes. This should be contrasted with the near horizon limit of usual extremal black holes, where one generically finds an AdS 2 factor, rather than an AdS 3 [16][17][18][19].…”

“…Nonetheless, one may perform a reduction of the gravity theory over the θψ part and observe that one obtains, as expected, a 3d Einstein gravity with negative cosmological constant. If the Newton constant of the 5d theory is denoted by G 5 the 3d Newton constant is G 3 = G 5 /(πℓ 2 ) and the AdS 3 radius is ℓ [14,15]. One may then use AdS 3 /CFT 2 duality and propose that low energy effective dynamics of 5d gravity over the metric (3.8) is described by a 2d CFT at central charge c = 3ℓ/(2G 3 ) = 3πℓ 3 /(2G 5 ).…”

Near-horizon extremal geometries: coadjoint orbits and quantization

“…2 For n = 0, near-horizon extreme Kerr is the unique metric in this class while for n = 1 there are other solutions, e.g. those obtained in the near horizon limit of extremal black rings or boosted Kerr strings [34,35].…”

“…or rings with k 2 = 1/k 1 [34,35,44]. Note that under SL(2, R) isometries which keep the t, r parts of the metric intact, rdt transforms by a closed form, rdt → rdt+dξ, where ξ depends on the details of the transformation.…”

Singly-spinning black rings in D = 5 U(1)3 supergravity

“…The black ring solution has an Extremal Vanishing Horizon (EVH) case for which the near-horizon geometry has an AdS 3 factor and is contained within the large class of near-horizon geometries that have been studied and classified in [25][26][27]. According to the proposed EVH/CFT correspondence, there is a two-dimensional CFT description of the low-energy excitations of the black ring in this case [28].…”