Sequences of Einstein-Yang-Mills-Dilaton Black Holes

Abstract

Einstein-Yang-Mills-dilaton theory possesses sequences of neutral static spherically symmetric black hole solutions. The solutions depend on the dilaton coupling constant $\gamma$ and on the horizon. The SU(2) solutions are labelled by the number of nodes $n$ of the single gauge field function, whereas the SO(3) solutions are labelled by the nodes $(n_1,n_2)$ of both gauge field functions. The SO(3) solutions form sequences characterized by the node structure $(j,j+n)$, where $j$ is fixed. The sequences of magnetically neutral solutions tend to magnetically charged limiting solutions. For finite $j$ the SO(3) sequences tend to magnetically charged Einstein-Yang-Mills-dilaton solutions with $j$ nodes and charge $P=\sqrt{3}$. For $j=0$ and $j \rightarrow \infty$ the SO(3) sequences tend to Einstein-Maxwell-dilaton solutions with magnetic charges $P=\sqrt{3}$ and $P=2$, respectively. The latter also represent the scaled limiting solutions of the SU(2) sequence. The convergence of the global properties of the black hole solutions, such as mass, dilaton charge and Hawking temperature, is exponential. The degree of convergence of the matter and metric functions of the black hole solutions is related to the relative location of the horizon to the nodes of the corresponding regular solutions.