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We present different Taub-NUT/Bolt-anti de Sitter (AdS) solutions in ashift-symmetric sector of Horndeski theory of gravity possessing nonminimalkinetic coupling of scalar fields to the Einstein tensor. In four dimensions,we find locally and asymptotically locally AdS solutions possessing nontrivialscalar field. In higher dimensions, analytical Taub-NUT/Bolt-AdS p-branes andsolitons are obtained, supported by the existence of p Horndeski scalar fieldswith axionic profile. The thermodynamical properties are studied throughEuclidean methods and it is found that the first law of thermodynamics issatisfied. Moreover, constraints on the parameter space of Horndeski gravityand NUT charge are obtained by demanding positivity of the mass, entropy, andspecific heat of the p-branes and soliton. We briefly comment on futureapplications in holography.

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