BMS${}_3$ 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 [SciPost Phys. 10, 022 (2021), [2010.07059]] that this model exhibits a symmetry under the $(2+1)$-dimensional Poincaré 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 Poincaré 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.

32 pages

References in corpus (13)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Notes on the BMS group in three dimensions: I. Induced representations
• The Weyl BMS group and Einstein's equations
• Notes on the BMS group in three dimensions: II. Coadjoint representation
• Geometric actions for three-dimensional gravity
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
• Black hole entropy from the boundary conformal structure in 3D gravity with torsion
• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• From black holes to baby universes in CGHS gravity
• On the Various Extensions of the BMS Group
• BMS Algebra, Double Soft Theorems, and All That

Cited by in corpus (5)

• Dynamical symmetries of homogeneous minisuperspace models
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC
• Polyharmonic Green Functions and Nonlocal BMS Transformations of a Free Scalar Field
• Hidden Symmetries in Gravity : Black holes and other minisuperspaces
• Dynamical axisymmetric compact objects in General Relativity