Discreteness of dyonic dilaton black holes

TL;DR

This paper classifies static spherically symmetric dyonic dilaton black holes, revealing a new class of solutions with discrete horizon properties that vary continuously with the dilaton coupling constant.

Contribution

It introduces a second class of black hole solutions with unique properties, expanding understanding beyond previously known special-coupling solutions.

Findings

Two classes of solutions identified for dyonic dilaton black holes.

New solutions exist for continuous coupling constants but discrete horizon dilaton values.

Multiple solutions can exist for a given coupling, distinguished by the dilaton's zeros.

Abstract

We show that there are two classes of solutions that describe static spherically symmetric dyonic dilaton black holes with two nonsingular horizons. The first class includes only the already known solutions that exist for a few special values of the dilaton coupling constant. Solutions belonging to the second class have essentially different properties. They exist for continuously varying values of the dilaton coupling constant, but arise only for discrete values of the dilaton field at the horizon. For each given value of the dilaton coupling constant, there may exist several such solutions differing by the number of zeros of the shifted dilaton function in the subhorizon region and separating the domains of singular solutions.