Curing black hole singularities with local scale invariance

TL;DR

This paper demonstrates that Weyl-invariant dilaton gravity can eliminate classical black hole singularities, replacing them with phase transitions and baby universes, which could impact the black hole information paradox.

Contribution

It introduces a Weyl-invariant gravity framework that removes classical singularities and proposes a new interior structure for black holes, differing from standard General Relativity.

Findings

Singularities correspond to phase transitions in Weyl symmetry.

Black holes may contain baby universes or white holes instead of singularities.

A critical mass exists where black hole size increases as mass decreases.

Abstract

We show that Weyl-invariant dilaton gravity provides a description of black holes without classical spacetime singularities. Singularities appear due to ill-behaviour of gauge fixing conditions, one example being the gauge in which theory is classically equivalent to standard General Relativity. The main conclusions of our analysis are: (1) singularities signal a phase transition from broken to unbroken phase of Weyl symmetry, (2) instead of a singularity there is a "baby-universe" or a white hole inside a black hole, (3) in the baby universe scenario there is a critical mass after which reducing mass makes black hole larger as viewed by outside observers, (4) if a black hole could be connected with white hole through the "singularity", this would require breakdown of (classical) geometric description, (5) the singularity of Schwarzschild BH solution is non-generic and so it is dangerous to rely on it in deriving general results. Our results may have important consequences for resolving issues related to information-loss puzzle. The theory we use is basically a completion of General Relativity, containing neither additional physical excitations nor higher-derivative terms, but requires physical scalar field such as Higgs field of Standard Model. Though quantum effects are still crucial and may change the proposed classical picture, a position of building quantum theory around essentially regular classical solutions normally provides a much better starting point.