Symmetries of the Black Hole Interior and Singularity Regularization

Abstract

We reveal an iso(2, 1) Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincaré group ISO(2, 1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS 2 . At the Lagrangian level, this symmetry corresponds to Möbius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger BMS 3 = Diff(S 1 ) ⋉ Vect(S 1 ) group, where S 1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincaré symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

Hidden symmetry of the static response of black holes: Applications to Love numbers

“…[41] that the Schwarzschild-(A)dS mechanics possesses a set of dynamical symmetries under the Poincaré group SL(2, R) ⋉ R 3 , extending previous results in Ref. [42]. In particular, the Schwarzschild background was shown to be covariant under the Möbius symmetry transformation provided the metric functions transform with a suitable conformal weight 7 .…”

Effective Quantum Dust Collapse via Surface Matching

“…In this paper special focus has been put on effective polymer models as symmetry reduced LQG models [1,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Without specifying a concrete model, it was already possible to deduce the qualitative properties of the collapsing surface.…”

“…A common way to study black holes in quantum gravity is to study eternal black holes [1,12,13,16,17,19,21,22,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]87], which is of course not the scenario that takes place in nature. Using the matching conditions (2.19) provides us with a strategy to extend the eternal black hole model to a dust collapse model according to the interpretation of Sec.…”

“…Similar efforts have been taken within the framework of spherically symmetric and static black holes, which are still simple due to a high amount of symmetries. The field of effective quantum descriptions of black holes in LQG is still active [1,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Besides LQG, also in other approaches of quantum gravity, non-singular solutions of black holes were studied as particular examples show, see e.g.…”

Symmetries and conformal bridge in Schwarzschild-(A)dS black hole mechanics

“…Preliminary results along that line have been obtained recently. By considering the anisotropic Kantowski-Sachs cosmological model, which describes the Schwarzschild interior mechanics, it was shown that the SL(2, R) symmetry group found in the isotropic case is enhanced to the three dimensional Poincaré group SL(2, R) ⋉ R 3 [28]. The charge algebra associated to this symmetry group allows one to reconstruct the black hole interior dynamics.…”