Asymptotically flat charged rotating dilaton black holes in higher dimensions

Abstract

We find a class of asymptotically flat slowly rotating charged black hole solutions of Einstein-Maxwell-dilaton theory with arbitrary dilaton coupling constant in higher dimensions. Our solution is the correct one generalizing the four-dimensional case of Horne and Horowitz [1]. In the absence of a dilaton field, our solution reduces to the higher dimensional slowly rotating Kerr-Newman black hole solution. The angular momentum and the gyromagnetic ratio of these rotating dilaton black holes are computed. It is shown that the dilaton field modifies the gyromagnetic ratio of the black holes.

Properties of rotating Einstein-Maxwell-dilaton black holes in odd dimensions

“…The same result was obtained when considering first order perturbations in the angular momentum for the charged static solutions in the EM case (h = 0) [14] …”

“…The curves formed by the gyromagnetic ratio g of the extremal black holes and by the gyromagnetic ratio g δj , Eq. (82), obtained for black holes in the static limit J → 0 [14], enclose the domain, where the gyromagnetic ratio can take its values. Since the extremal and the 'static' curve are very close to each other, the 'static' values represent a good approximation for a given value of q. Consequently, the gyromagnetic ratio is not well resolved for the non-extremal sets of solutions in the figure.…”

“…4(c), we note, that it attains the perturbative value g δq = 3 [10] for small q, independent of the dilaton coupling constant h. For a fixed value of h, the curves formed by the gyromagnetic ratio g of the extremal black holes and by the gyromagnetic ratio g δj , Eq. (82), obtained for black holes in the static limit J → 0 [14], enclose the domain, where the gyromagnetic ratio can take its values.…”

“…However, it still represents an important limiting value for EM and EMd black holes, attained for small values of the charge to mass ratio q. In fact, in the EMd case (h = 0) first order perturbations in the angular momentum for the charged static solutions yield, in our conventions in terms of q = Q/M and a generic dilaton coupling h, the expression [14] …”

“…In the simplest case this leads to electrically charged Einstein-Maxwell-dilaton (EMd) black holes for a particular value of the dilaton coupling constant, h = h KK [6,7,8,9]. For general dilaton coupling constant h, however, rotating EMd black hole solutions or their Einstein-Maxwell (EM) counterparts need either perturbative techniques [10,11,12,13,14,15,16] or numerical analysis [17,18,19].…”