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“Triangular” extremal dilatonic dyons. (English) Zbl 1343.83037
Summary: Explicit dyonic solutions in four-dimensional Einstein-Maxwell-dilaton theory are known only for three particular values of the dilaton coupling constant: $$a=0,1,\sqrt{3}$$. However, numerical evidence was presented on existence of dyons admitting an extremal limit in theories with more general sequence of dilaton couplings $$a=\sqrt{n(n+1)/2}$$ labeled by an integer {$$n$$. Apart from the lower members $$n=0,1,2$$, this family of theories does not have motivation from supergravity/string theory, and analytical origin of the above sequence remained unclear so far. We fill the gap showing that this formula follows from analyticity of the dilaton function at the $$\mathrm{AdS}_2 \times S^2$$ event horizon of the extremal dyonic black hole, with $$n$$ being the leading dilaton power in the Taylor expansion. We also derive generalization of this rule for asymptotically anti-de Sitter dyonic black holes with spherical, planar and hyperbolic topology of the horizon.}

##### MSC:
 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83C57 Black holes 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 83E50 Supergravity
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