"Triangular" extremal dilatonic dyons

Abstract

Explicit dyonic dilaton black holes of the four-dimensional Einstein-Maxwell-dilaton theory are known only for two particular values of the dilaton coupling constant $a=1,\sqrt{3}$, while for other $a$ numerical evidence was presented earlier about existence of extremal dyons in theories with the discrete sequence of dilaton couplings $a=\sqrt{n(n+1)/2}$ with integer $n$. Apart from the lower members $n=1,2$, this family of theories does not have motivation from supersymmetry or higher dimensions, and so far the above quantization rule has not been derived analytically. We fill this gap showing that this rule follows from analyticity of the dilaton at the $Ad{S}_2\times S^2$ event horizon with $n$ being the leading dilaton power in the series expansion. We also present generalization for asymptotically anti-de Sitter dyonic black holes with spherical, plane and hyperbolic topology of the horizon.

An error in Sec IV and misprints throughout the paper are corrected, one figure added, other figures replaced

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• STU Black Holes and SgrA*
• Higher-$n$ triangular dilatonic black holes
• Discreteness of dyonic dilaton black holes
• Mass And Force Relations For Einstein-Maxwell-Dilaton Black Holes
• Nutty Kaluza-Klein dyons revisited
• On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes
• Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field
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