Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

Understand

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions.

• We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon.
• We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.