Thermodynamics of dyonic black holes with Thurston horizon geometries

TL;DR

This paper constructs and analyzes five-dimensional dyonic black holes with Thurston geometries, exploring their thermodynamics, charges, and extensions with hyperscaling violation, revealing proportional electric and magnetic charges and conditions for purely magnetic solutions.

Contribution

It introduces new dyonic black hole solutions with Thurston geometries and examines their thermodynamic properties and charge relations, including hyperscaling violations.

Findings

Dyonic solutions exhibit Lifshitz scaling with arbitrary dynamical exponent.

Electric and magnetic charges are proportional, resembling Chern-Simons vortices.

Purely magnetic solutions occur at specific hyperscaling violating parameters.

Abstract

In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatonic-like couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian formalism, the mass, the electric and magnetic charges are explicitly computed. Interestingly enough, the dyonic solutions behave like Chern-Simons vortices in the sense that their electric and magnetic charges turn to be proportional. The extension with an hyperscaling violating factor is also scrutinized where we notice that for specific values of the violating factor, purely magnetic solutions are possible.