Research Article Electrostatics in the Surroundings of a Topologically Charged Black Hole in the Brane Alexis Larrañaga, 1 Natalia Herrera, 2 and Sara Ramirez 2 1 National Astronomical Observatory, National University of Colombia, Bogota 11001000, Colombia 2 Department of Physics, National University of Colombia, Bogota 11001000, Colombia Correspondence should be addressed to Alexis Larra˜ naga; ealarranaga@unal.edu.co Received 27 December 2013; Revised 21 January 2014; Accepted 23 January 2014; Published 27 February 2014 Academic Editor: Christian Corda Copyright © 2014 Alexis Larra˜ naga et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te publication of this article was funded by SCOAP 3 . We determine the expression for the electrostatic potential generated by a point charge held stationary in the topologically charged black hole spacetime arising from the Randall-Sundrum II braneworld model. We treat the static electric point charge as a linear perturbation on the black hole background and an expression for the electrostatic multipole solution is given: PACS: 04.70.-s, 04.50.Gh, 11.25.-w, 41.20.-q, 41.90.+e. 1. Introduction Te idea of our universe as a brane embedded in a higher dimensional spacetime has recently attracted attention. According to the braneworld scenario, the physical felds (electromagnetic, Yang-Mills, etc.) in our 4-dimensional universe are confned to the three-brane and only gravity propagates in the bulk spacetime. One of the most interesting scenarios is Randall-Sundrum II model in which it is consid- ered a Z 2 -symmetric, 5-dimensional, asymptotically anti-de- Sitter bulk [1] and our brane is identifed as a domain wall. Te 5-dimensional metric can be written in the general form  2 = −()  ]    ] +  2 and due to the appearance of the warp factor, it reproduces a large hierarchy between the scale of particle physics and gravity. Moreover, even if the ffh dimension is uncompactifed, standard 4-dimensional gravity on the brane is reproduced. However, due to the cor- rection terms coming from the extradimensions, signifcant deviations from general relativity may occur at high energies [2–4]. As is well known, in general relativity the exterior spacetime of a spherical compact object is described by Schwarzschild solution. In the braneworld scenario, the high energy corrections to the energy density together with Weyl stresses from bulk gravitons imply that the exterior metric of a spherical compact object on the brane is no longer described by Schwarzschild metric. In fact, black hole solutions in the braneworld model are particularly interesting because they have considerably richer physical aspects than black holes in general relativity [5–11]. Te frst solutions describing static and spherically symmetric exterior vacuum solutions of the braneworld model were proposed by Dadhich et al. [12] and Germani and Maartens [13] and later they were generalised by Chamblin et al. [14] and revisited by Sheykhi and Wang [15]. Tis kind of solutions carries a topological charge arising from the bulk Weyl tensor and the line element resembles Reissner-N¨ ordstrom solution, with the tidal Weyl parameter playing the role of the electric charge. In order to obtain this solution, there was the null energy condition imposed on the three-brane for a bulk having nonzero Weyl curvature. On the other hand, the generation of an electromagnetic feld by static sources in black hole backgrounds has been considered in several papers beginning with the studies of Copson [16], Cohen and Wald [17], and Hanni and Rufni [18] where they discussed the electric feld of a point charge in Schwarzschild background. Aferwards, Petterson [19] and later Linet [20] studied the magnetic feld of a current loop surrounding a Schwarzschild black hole. More recently, similar studies have been performed in other background Hindawi Publishing Corporation Advances in High Energy Physics Volume 2014, Article ID 146094, 6 pages http://dx.doi.org/10.1155/2014/146094