Scalarization-like mechanism through spacetime anisotropic scaling symmetry

TL;DR

This paper introduces a new family of exact Lifshitz black hole solutions with scalar fields, demonstrating their thermodynamic properties and suggesting a spontaneous scalarization mechanism due to anisotropic scaling symmetry breaking.

Contribution

It presents novel Lifshitz black hole solutions with scalar fields in arbitrary dimensions, linking them to known solutions and analyzing their thermodynamics and scalarization conditions.

Findings

Solutions are asymptotically Lifshitz with arbitrary z≥1.

Scalar field emergence is linked to anisotropic scaling symmetry breaking.

Thermodynamics satisfies the first law and Smarr formula, with scalarization conditions verified.

Abstract

We present a new family of exact black hole configurations, which is a solution to a generalized Einstein-Maxwell-Dilaton setup in arbitrary dimension. These solutions are asymptotically Lifshitz for any dynamical critical exponent $z\geq 1$. It turns out that the existence of a nontrivial scalar field is a direct consequence of breaking the spacetime isotropic scaling symmetry. This black hole family accepts various interesting limits that link it to well-known solutions in both the isotropic and anisotropic cases. We study the thermodynamics of these field configurations showing that the first law is satisfied and providing the corresponding Smarr formula, both of these relations account for an electric contribution. Furthermore, we show that for a certain parameter region, the anisotropic field configuration with a nonzero scalar field is thermodynamically preferred. This observation, together with a direct verification of the so-called scalarization conditions, suggest that the emergence of the dilaton field is due to a mechanism similar to spontaneous scalarization.