Formation of shell-crossing singularities in effective gravitational collapse models with bounded and unbounded polymerizations

TL;DR

This paper investigates shell-crossing singularities in effective polymerized LTB models, showing that in models with a bounce, SCS are unavoidable, whereas in models without a bounce and unbounded polymerization, SCS can be avoided.

Contribution

It extends analysis to asymmetric bounce models and unbounded polymerization models, revealing conditions for the formation or avoidance of SCS.

Findings

SCS are unavoidable in asymmetric bouncing models with inhomogeneous dust.

No SCS form in models without a bounce and unbounded polymerization for decreasing dust profiles.

Classical theory's avoidance of SCS by initial data is mirrored in certain polymer models.

Abstract

We extend the investigation into the formation of shell-crossing singularites (SCS) in effective polymerized LTB models to the LQG-inspired asymmetric bounce model, as well as to effective LTB models based on the solutions of Bardeen and Hayward, in which no bounce occurs. While the asymmetric bouncing model belongs to the class of bounded polymerization functions, the latter models feature unbounded polymerization functions. Our results show that, similar to the symmetric bouncing model, for the asymmetric bouncing model SCS are unavoidable for inhomogeneous dust profiles. In contrast, for models without a bounce and with unbounded polymerization functions, no SCS form for inhomogeneous, decreasing dust profiles -- a situation that resembles classical theory, in which SCS can also be avoided by a suitable choice of initial data.