Regularized Black Holes from Doubled FLRW Cosmologies

TL;DR

This paper introduces a deformation of the mini-superspace Hamiltonian for black holes, resulting in non-singular metrics that can be viewed as superpositions of two homogeneous FRW cosmologies with perfect fluids.

Contribution

It identifies a continuous deformation of the black hole mini-superspace Hamiltonian that enhances its symmetry from Poincaré to SO(3,1) or SO(2,2), leading to non-singular black hole solutions.

Findings

Deformed dynamics correspond to superpositions of two FRW cosmologies.

Resulting black hole metrics are non-singular.

Symmetry group extended from Poincaré to SO(3,1) or SO(2,2).

Abstract

Reduced general relativity for four-dimensional spherically-symmetric stationary space-times, more simply called the black hole mini-superspace, was shown in previous work to admit a symmetry under the three-dimensional Poincar\'e group ISO(2,1). Such a non-semi-simple symmetry group usually signals that the system is a special case of a more general model admitting a semi-simple Lie group symmetry. We explore here possible modifications of the Hamiltonian constraint of the mini-superspace. We identify in particular a continuous deformation of the dynamics that lifts the degeneracy of the Poincar\'e group and leads to a SO(3,1) or SO(2,2) symmetry. This deformation is not related to the cosmological constant. We show that the deformed dynamics can be represented as the superposition of two non-interacting homogeneous FRW cosmologies, with flat slices filled with perfect fluid. The resulting modified black hole metrics are found to be non-singular.