Higher-$n$ triangular dilatonic black holes

Abstract

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete ("triangular") values of the dilaton coupling constant $a=\sqrt{n(n+1)/2}$. From this sequence only $n=1,2$ members were known analytically so far. We present two new $n=3,5$ triangular solutions for the theory with different dilaton couplings $a,b$ in electric and magnetic sectors in which case the quantization condition reads $ab=n(n+1)/2$. These are derived via the Toda chains for $B_2$ and $G_2$ Lie algebras. Solutions are found in the closed form in general $D$ space-time dimensions. They satisfy the entropy product rules and have negative binding energy in the extremal case.

Acknowledgement corrected

References in corpus (3)

• Dilatonic dyon-like black hole solutions in the model with two Abelian gauge fields
• "Triangular" extremal dilatonic dyons
• Black holes as generalised Toda molecules

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• Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field