Finite conformal quantum gravity and spacetime singularities

TL;DR

This paper demonstrates that a class of finite, conformally invariant quantum gravity theories can resolve spacetime singularities, including black holes, by leveraging Weyl symmetry at both classical and quantum levels.

Contribution

It introduces a range of anomaly-free, conformally invariant gravitational theories that can eliminate spacetime singularities through Weyl symmetry.

Findings

Weyl conformal invariance can tame all classical spacetime singularities.

Explicit singularity-free black hole solutions are constructed within these theories.

A singularity theorem applies to a broad class of weakly non-local theories.

Abstract

We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.