Masking singularities in Weyl gravity and Ricci flows

TL;DR

This paper explores how Weyl gravity can produce various cosmological and wormhole solutions with masked singularities, and investigates their relation to Ricci flows and potential implications for quantum gravity theories.

Contribution

It demonstrates that singularities in Weyl gravity solutions can be masked and links certain solutions to Ricci flows, offering insights into quantum gravity modeling.

Findings

Singularities can be masked in Weyl gravity solutions.

Certain metrics form Ricci flows.

Discussion on Weyl gravity's relevance to quantum gravity.

Abstract

Within vacuum Weyl gravity, we obtain a solution by which, using different choices of the conformal factor, we derive metrics describing (i)~a bounce of the universe; (ii)~toroidal and spherical wormholes; and (iii)~a change in metric signature. It is demonstrated that singularities occurring in these systems are "masked". We give a simple explanation of the possibility of masking the singularities within Weyl gravity. It is shown that in the first and third cases the three-dimensional metrics form Ricci flows. The question of the possible applicability of conformal Weyl gravity as some phenomenological theory in an approximate description of quantum gravity is discussed.