BMS3 mechanics and the black hole interior

Abstract

The spacetime in the interior of a black hole can be described by an homogeneous line element, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We have shown in Geiller et al (2021 SciPost Phys. 10 022) that this model exhibits a symmetry under the (2 + 1)-dimensional Poincaré group. Here we extend the Poincaré transformations to the infinite-dimensional BMS3 group. Although the black hole model is not invariant under those extended transformations, we can write it as a geometric action for BMS3, where the configuration space variables are elements of the algebra and the equations of motion transform as coadjoint vectors. The BMS3 symmetry breaks down to its Poincaré subgroup, which arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS2 JT gravity, although in the present case there is no direct interpretation in terms of boundary symmetries. This observation, together with the fact that other lower-dimensional gravitational models (such as the BTZ black hole) possess the same broken BMS3 symmetries, provides yet another illustration of the ubiquitous role played by this group.