New Taub-NUT Black Holes with Massive Spin-2 Hair

TL;DR

This paper extends Einstein gravity with quadratic curvature terms to discover new Taub-NUT black holes with massive spin-2 hair, using stability analysis and numerical methods to identify and construct these novel solutions.

Contribution

It introduces a method to find and numerically construct new Taub-NUT black holes with massive spin-2 hair arising from quadratic curvature extensions.

Findings

Existence of two new Taub-NUT black holes for certain parameters

Identification of bifurcation points from Ricci-flat solutions

Presence of up to three Taub-NUT black holes at a given temperature

Abstract

We consider Einstein gravity extended with quadratic curvature invariants, where the well-known Ricci-flat Taub-NUT black hole remains a solution. An analysis of the unstable Lichnerowicz modes in the Taub-NUT background enables us to identify the mass and NUT parameters (m,n) where new Taub-NUT black holes can emerge. We then adopt numerical technique to construct these new Taub-NUT black holes that bifurcate away from the Ricci-flat ones. Unlike the Ricci-flat Taub-NUT, there can exist two new black holes for an appropriate given temperature, making it a total of three if we include the Ricci-flat one.