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.
Highlights
Stationary nonsingular Euclidean solutions of the Yang–Mills equations with finite action— known as instantons—are extremely important in quantum field theories [1,2]
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
They represent nonperturbative effects at the quantum level and they appear as the leading contribution to physical observables
Summary
Stationary nonsingular Euclidean solutions of the Yang–Mills equations with finite action— known as instantons—are extremely important in quantum field theories [1,2]. The Taub-bolt solution, on the other hand, is endowed with a horizon and it resembles Euclidean black holes [30] Due to this, their thermodynamic properties is an interesting and active research area, ranging from their extended phase structure to holographic heat engines [21,22,31,32,33,34,35]. The aim of this work is to show that Taub-NUT/bolt-AdS solutions exist in a particular sector of Horndeski gravity To this end, we focus on the nonminimal derivative coupling of the scalar field to the Einstein’s tensor and found different solutions.
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