Consistent Gauge Conditions for Dust-Shell Dynamics in Effective Quantum Gravity

TL;DR

This paper develops a systematic method for choosing consistent gauge conditions in effective quantum gravity models involving dust shells, improving the analysis of shell-crossing singularities and shock dynamics.

Contribution

It introduces a new gauge selection method for dust-shell dynamics in effective quantum gravity, verified through classical GR and numerical simulations, aligning with Israel junction conditions.

Findings

Incompatible gauges like Painlevé-Gullstrand and Schwarzschild with dust shells.

The new gauge method resolves previous difficulties in shell-crossing analysis.

Framework facilitates studying shock dynamics in quantum black-hole models.

Abstract

Previous analyses of shocks generated by shell-crossing singularities are affected by inappropriate gauge choices, and no systematic method is available for selecting a consistent gauge. In this work, we develop such a method for effective quantum gravity coupled to a dust shell. We illustrate it in classical general relativity and verify it numerically, with results in agreement with the Israel junction condition. We also show that gauges such as the Painlev\'e-Gullstrand and Schwarzschild ones are incompatible with the presence of a dust shell when imposed on the whole spatial slice. This explains the difficulties in previous treatments. The framework developed here provides a basis for studying shell-crossing singularities and shock dynamics in generally covariant effective black-hole models.