Shaping black holes with free fields

TL;DR

This work constructs and analyzes static AdS black holes dressed by free scalar and $p$-form fields across diverse horizon geometries, including Einstein, Einstein–Kähler, and product spaces. Using a unified metric Ansatz with isotropy and homogeneity constraints on the horizon ${\\mathcal{H}}$, the authors derive the lapse function $V(r)$ in terms of the external stress-energy density $\\epsilon(r)$ and demonstrate how single and multiple form fields—along with axions—shape horizon topology, regularize singularities, and yield dyonic solutions. They develop explicit solutions for electric, magnetic, and dyonic charges, including spacetime-filling forms that act as effective cosmological constants, and study their thermodynamics via Euclidean path integrals and the Hamiltonian approach, establishing the first law with brane charges and computing the Gibbs free energy with background subtraction. The results open pathways for holographic applications and higher-dimensional generalizations, including potential stabilization of otherwise unstable topologies and extensions to rotating or more intricate matter contents. Overall, the paper provides a broad, constructive framework for shaping black holes with free fields through fluxes on horizon geometries and analyzes the resulting thermodynamics and phase structure.

Abstract

Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant Λ. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when Λ<0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular -- rather than singular -- small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.