Higher-$n$ triangular dilatonic black holes

TL;DR

This paper introduces new higher-n triangular dilatonic black hole solutions in various dimensions, expanding the known analytical solutions for specific dilaton couplings using Toda chain methods, with implications for black hole entropy and stability.

Contribution

It provides the first analytical solutions for n=3 and n=5 triangular dilatonic black holes with different electric and magnetic couplings, derived via Toda chains for specific Lie algebras.

Findings

Solutions are expressed in closed form for arbitrary dimensions.

Solutions satisfy entropy product rules.

Extremal solutions have negative binding energy.

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 $a b = n (n + 1)/2$. 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.