Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

TL;DR

This paper constructs infinite-dimensional families of non-singular stationary black hole solutions with matter fields in anti-de Sitter space, using complex elliptic systems to extend known solutions with a negative cosmological constant.

Contribution

It introduces a novel elliptic system approach to generate a wide class of non-singular black hole solutions with matter fields in AdS space, expanding the solution space significantly.

Findings

Existence of infinite-dimensional families of black hole solutions.

Solutions include the standard AdS conformal structure at infinity.

Method applies to complex-valued tensor fields in Einstein-matter equations.

Abstract

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-$f(R)$ equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.