NUTs and bolts beyond Lovelock

TL;DR

This paper constructs new higher-curvature gravity solutions in four and six dimensions, generalizing known Einstein solutions, and analyzes their thermodynamic properties, revealing novel phenomena like regular bolts and phase transitions.

Contribution

It provides the first generalizations of Einstein gravity Taub-NUT/bolt solutions in higher-curvature theories and explores their thermodynamics, including solutions with quartic quasi-topological terms.

Findings

New solutions with various base spaces in 4D and 6D higher-curvature theories.

Existence of regular bolts and critical points in the solutions.

Re-entrant phase transitions and unique thermodynamic behaviors.

Abstract

We construct a plethora of new Euclidean AdS-Taub-NUT and bolt solutions of several four- and six-dimensional higher-curvature theories of gravity with various base spaces $\mathcal{B}$. In $D=4$, we consider Einsteinian cubic gravity, for which we construct solutions with $\mathcal{B}=\mathbb{S}^2,\mathbb{T}^2$. These represent the first generalizations of the Einstein gravity Taub-NUT/bolt solutions for any higher-curvature theory in four dimensions. In $D=6$, we show that no new solutions are allowed for any Generalized quasi-topological gravity at cubic order. They exist however when we consider quartic Quasi-topological and Generalized quasi-topological terms, for which we construct new solutions with $\mathcal{B}=\mathbb{CP}^2,\mathbb{S}^2\times\mathbb{S}^2,\mathbb{S}^2\times\mathbb{T}^2,\mathbb{T}^2\times\mathbb{T}^2$. In all cases, the solutions are characterized by a single metric function, and they reduce to the corresponding ones in Einstein gravity when the higher-curvature couplings are set to zero. While the explicit profiles must be constructed numerically (except for a few cases), we obtain fully analytic expressions for the thermodynamic properties of all solutions. The new solutions present important differences with respect to Einstein gravity, including regular bolts for arbitrary values of the NUT charge, critical points, and re-entrant phase transitions.