More on near-horizon charges black holes with gravitational hair in three dimensions

Abstract

With the aim of continuing the exploration of near-horizon charges in higher-curvature gravity, searching for sectors leading to universal behaviors, we first provide a thorough revision and formulae of the covariant phase-space method applied to arbitrary gravitational theories containing up to quartic terms in the Riemann tensor in arbitrary dimension. These results can be applied in diverse setups, in particular in the context of $\alpha'$ corrections to String Theory, where it is known that in Type II theories, the first correction to the Einstein-Hilbert Lagrangian goes as $\alpha'^3 \mathcal{R}^4$. Then, we test these formulae for near horizon asymptotic symmetries of the rotating BTZ spacetime where the first law of black hole thermodynamics is consistently recovered. It was recently realized that a subset of these higher curvature gravities do admit black holes with gravitational hair, whose entropy can be microscopically accounted for, as is the case of New Massive Gravity. In this case, the four maximally symmetric vacua of the theory coincide, and the theory acquires an extra gauge symmetry when linearized around such a vacuum. We study the near-horizon asymptotic symmetries and compute the associated charges, both in the static and rotating hairy black holes, extending up to $\mathcal{R}^4$, a work that was previously done only up to a quadratic term. In order to allow for a continuous lecture on the work, we report the explicit expressions of the general Lagrangians in the appendices.