New Taub-NUT black holes with massive spin-2 hair

We consider Einstein gravity extended with quadratic curvature invariants, within which 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 techniques to construct these new Taub-NUT black holes, which 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.