Full phase space of charged black-hole existence and stability

Characterize the full phase space governing the existence and stability of electrically and magnetically charged black-hole solutions in vector Horndeski theories with non-minimal double-dual-Riemann-tensor–electromagnetic coupling.

Background

The paper studies static, spherically symmetric electrically and magnetically charged black holes in a vector Horndeski theory, whose action includes a four-derivative coupling between the electromagnetic field strength and the double-dual Riemann tensor. The authors analyze the background solutions, derive perturbation equations, establish relevant no-ghost and gradient-stability conditions, and compute quasinormal-mode spectra within the physically admissible parameter regions.

Despite these analyses, the complete phase space of black-hole solutions—including the full ranges of charge and coupling parameters, the existence of horizons versus naked singularities, and all stability properties—has not been characterized. The cited prior work addressed linear perturbation equations and selected ghost and gradient instabilities, but the paper identifies the broader existence-and-stability classification as unresolved.