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

We obtain magnetic black-hole solutions in arbitrary $n(\ge 4)$ 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 ${\ma M}^{2} \times {\ma K}^{n-2}$, where ${\ma K}^{n-2}$ 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 Jebsen-Birkhoff theorem for the magnetic solution in the case where the orbit of the warp factor on ${\ma K}^{n-2}$ 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 ${\ma K}^{n-2}$ 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.