Hairy Taub-NUT/Bolt-AdS solutions in Horndeski theory

TL;DR

This paper introduces new Taub-NUT/Bolt-AdS solutions within Horndeski gravity, analyzing their properties and thermodynamics, and discusses implications for holography.

Contribution

It provides novel analytical Taub-NUT/Bolt-AdS solutions in Horndeski theory with scalar fields, extending known solutions to higher dimensions and exploring their thermodynamics.

Findings

Solutions are asymptotically locally AdS with nontrivial scalar fields.

Thermodynamics satisfies the first law, with positive mass, entropy, and specific heat.

Constraints on parameters ensure physical viability of solutions.

Abstract

We present different Taub-NUT/Bolt-anti de Sitter (AdS) solutions in a shift-symmetric sector of Horndeski theory of gravity possessing nonminimal kinetic coupling of scalar fields to the Einstein tensor. In four dimensions, we find locally and asymptotically locally AdS solutions possessing nontrivial scalar field. In higher dimensions, analytical Taub-NUT/Bolt-AdS p-branes and solitons are obtained, supported by the existence of p Horndeski scalar fields with axionic profile. The thermodynamical properties are studied through Euclidean methods and it is found that the first law of thermodynamics is satisfied. Moreover, constraints on the parameter space of Horndeski gravity and NUT charge are obtained by demanding positivity of the mass, entropy, and specific heat of the p-branes and soliton. We briefly comment on future applications in holography.