BMS$_3$ Mechanics and the Black Hole Interior

TL;DR

This paper reveals that the interior black hole spacetime can be modeled as a one-dimensional mechanical system exhibiting a broken BMS$_3$ symmetry, linking black hole physics with infinite-dimensional symmetry groups.

Contribution

It interprets the black hole interior model as a geometric action for BMS$_3$, showing how the Poincaré symmetry emerges as a stabilizer within this framework.

Findings

The model exhibits a broken BMS$_3$ symmetry.

The Poincaré subgroup stabilizes the vacuum orbit.

Similar symmetries are found in other lower-dimensional gravity models.

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 [SciPost Phys. 10, 022 (2021), [2010.07059]] that this model exhibits a symmetry under the $(2+1)$-dimensional Poincar\'e group. Here we explain how this can be understood as a broken infinite-dimensional BMS$_3$ symmetry. This is done by reinterpreting the action for the model as a geometric action for BMS$_3$, where the configuration space variables are elements of the algebra $\mathfrak{bms}_3$ and the equations of motion transform as coadjoint vectors. The Poincar\'e subgroup then arises as the stabilizer of the vacuum orbit. This symmetry breaking is analogous to what happens with the Schwarzian action in AdS$_2$ 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 BMS$_3$ symmetries, provides yet another illustration of the ubiquitous role played by this group.