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Static M-horizons

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Abstract

We determine the geometry of all static black hole horizons of M-theory pre-serving at least one supersymmetry. We demonstrate that all such horizons are either warped products \( {\mathbb{R}^{1,1}}{ \times_w}\mathcal{S} \) or \( Ad{S_2}{ \times_w}\mathcal{S} \), where \( \mathcal{S} \) admits an appropriate Spin(7) or SU(4) structure respectively; and we derive the conditions imposed by supersymmetry on these structures. We show that for electric static horizons with Spin(7) structure, the near horizon geometry is a product \( {\mathbb{R}^{1,1}} \times \mathcal{S} \), where \( \mathcal{S} \) is locally a compact Spin(7) holonomy manifold. For electric static solutions with SU(4) structure, we show that the horizon section \( \mathcal{S} \) is a circle fibration over an 8-dimensional Kähler manifold which satisfies an additional condition involving the Ricci scalar and the length of the Ricci tensor. Solutions include AdS 2×S 3×CY 6 as well as many others constructed from taking the 8-dimensional Kähler manifold to be a product of Kähler-Einstein and Calabi-Yau spaces.

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  1. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, UK

    Jan Gutowski & George Papadopoulos

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  1. Jan Gutowski
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  2. George Papadopoulos
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Correspondence to Jan Gutowski.

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Gutowski, J., Papadopoulos, G. Static M-horizons. J. High Energ. Phys. 2012, 5 (2012). https://doi.org/10.1007/JHEP01(2012)005

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