Black strings with a negative cosmological constant: inclusion of electric charge and rotation

Abstract

We generalize the vacuum static black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature, by including an electromagnetic field. These higher-dimensional configurations have no dependence on the 'compact' extra dimension, while their boundary topology is the product of time andRotating generalizations of the even dimensional black string configurations are considered as well. Different from the static, neutral case, no regular limit is found for a vanishing event horizon radius. We explore numerically the general properties of such classical solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. We find that the thermodynamics of the black strings follows the pattern of the corresponding black hole solutions in AdS backgrounds.

Black strings in AdS5

“…If the magnetic charge assumes a certain value given in terms of the inverse gauge coupling constant (corresponding to a twisting of the dual super Yang-Mills theory), the conformal anomalies coming from the background curvature and those arising from the coupling to external gauge fields exactly cancel. 2 The study of their thermodynamics shows in the canonical ensemble (fixed magnetic charge) a van der Waals-Maxwell phase structure similar to the one of the Reissner-Nordström-AdS black holes [9,10] and electrically charged black strings in AdS 5 [20]: for small magnetic charges, we find two coexisting black string phases separated by a first order phase transition, which disappears at a critical point as we increase the charge.…”

“…Not much is known on the black hole phases in this case; uniform, neutral black strings with S 2 × S 1 topology have been found by Copsey and Horowitz in [18] and then generalized to higher dimensions and arbitrary S by Mann, Radu and Stelea in [19]. Electric charge and angular momentum were included in [20], while non-abelian black string solution (but also abelian U(1)) were obtained in [21]. These solutions are typically numerical, since in presence of a cosmological constant the black strings cannot be constructed by taking a direct product with a circle, and the differential equations they verify cannot be solved analytically.…”

5D black holes and non-linear sigma models

“…55) 56) and using (3.21), it is straightforward to check that the algebra of constraints is first class,…”

Spacetime Topology and the Laws of Black Hole-Soliton Mechanics

“…To derive a general first law in this setting it may be useful to study explicit examples of gravitational solitons in AdS 5 [24] and their physical properties [25]. Extending beyond the case of globally AdS 5 asymptotics, one can also consider the thermodynamics of black string spacetimes with a negative cosmological constant with compact spatial directions in the asymptotic region [26].…”