Magnetic black holes with higher-order curvature and gauge corrections in even dimensions

Abstract

We obtain magnetic black-hole solutions in arbitrary n(≥ 4) even dimensions for an action given by the Einstein-Gauss-Bonnet-Maxwell-Λ pieces with the F 4 gauge-correction terms. This action arises in the low energy limit of heterotic string theory with constant dilaton and vanishing higher form fields. The spacetime is assumed to be a warped product M 2 × K n−2 , where K n−2 is a (n − 2)-dimensional Einstein space satisfying a condition on its Weyl tensor, originally considered by Dotti and Gleiser. Under a few reasonable assumptions, we establish the generalized JebsenBirkhoff theorem for the magnetic solution in the case where the orbit of the warp factor on K n−2 is non-null. We prove that such magnetic solutions do not exist in odd dimensions. In contrast, in even dimensions, we obtain an explicit solution in the case where K n−2 is a product manifold of (n − 2)/2 two-dimensional maximally symmetric spaces with the same constant warp factors. In this latter case, we show that the global structure of the spacetime sharply depends on the existence of the gauge-correction terms as well as the number of spacetime dimensions.

Generalized charged Nariai solutions in arbitrary even dimensions with multiple magnetic charges

“…It is also worth pointing out that whereas the solution presented in Refs. [18,19] admits no magnetic charge at all, which is related to the fact that the second Betti number of the sphere S n−2 is different from zero only if n = 4 [26], the solution obtained here has several magnetic charges. This interesting feature makes these metrics a rich arena for studying the physics of higher-dimensional spacetimes.…”

“…Moreover, the cases q 2 = 0 (purely electric) and q 1 = 0 (purely magnetic) of this black hole solution can be attained in the limit of Einstein-Maxwell theory from the solutions found in Ref. [26].…”

“…Second, note that the additive constant term in the function f (r) is different from 1 if n = 4, and this constant factor cannot be modified by a coordinate transformation. Moreover, a higherdimensional Schwarzschild metric possessing a magnetic charge does not exist, which is related to the fact that the second Betti number of the sphere S n−2 is different from zero only if n = 4 [26]. Regarding the magnetic charge q 2 , it is also worth stressing that the sign of in front of q 2 2 in Eq.…”

Integrability of the Dirac equation on backgrounds that are the direct product of bidimensional spaces

“…These black hole solutions, that possess electric and magnetic charge, have been obtained in Refs. [15,24,25] and are given by…”

Lifshitz black holes in Brans-Dicke theory

“…where Q m is a real constant [41,42]. The Maxwell invariant scalar is given as 26) while the non-zero components of T (em) µ ν are given by…”