Finite Conformal Quantum Gravity and Nonsingular Spacetimes

TL;DR

This paper demonstrates that certain finite quantum gravity theories are conformally invariant and can produce nonsingular spacetimes, including black holes and cosmological models, by leveraging Weyl symmetry to resolve classical singularities.

Contribution

It explicitly constructs anomaly-free, conformally invariant quantum gravity theories that admit nonsingular black hole and cosmological solutions, extending classical results to quantum regimes.

Findings

Existence of singularity-free black hole solutions conformally related to Schwarzschild

Demonstration that FRW and BKL spacetimes are conformally equivalent to regular spacetimes

Proof that gravitational collapse solutions can be nonsingular in conformal quantum gravity

Abstract

We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions conformally equivalent to the Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve the classical equations of motion, are conformally equivalent to regular spacetimes. Finally, we prove that the Oppenheimer-Volkov gravitational collapse is a an exact (singularity-free) solution of the non-local conformally invariant theory compatible with the bounce paradigm.