Charged Taub-NUT solution in Lovelock gravity with generalized Wheeler polynomials

TL;DR

This paper extends Wheeler's method to stationary spacetimes in Lovelock gravity, deriving a Taub-NUT solution in eight dimensions coupled to Maxwell fields, with the NUT parameter generalizing Wheeler polynomials.

Contribution

It introduces a generalized approach for static and stationary solutions in Lovelock gravity, specifically deriving a new Taub-NUT solution in higher dimensions.

Findings

Derived a Taub-NUT solution in eight-dimensional Lovelock gravity.

Explicitly included Maxwell fields with general integration constants.

Showed how the NUT parameter generalizes Wheeler polynomials.

Abstract

Wheeler's approach to finding exact solutions in Lovelock gravity has been predominantly applied to static spacetimes. This has led to a Birkhoff's theorem for arbitrary base manifolds in dimensions higher than four. In this work, we generalize the method and apply it to a stationary metric. Using this perspective, we present a Taub-NUT solution in eight-dimensional Lovelock gravity coupled to Maxwell fields. We use the first-order formalism to integrate the equations of motion in the torsion-free sector. The Maxwell field is presented explicitly with general integration constants, while the background metric is given implicitly in terms of a cubic algebraic equation for the metric function. We display precisely how the NUT parameter generalizes Wheeler polynomials in a highly nontrivial manner.