Hyperbolicity in scalar-Gauss-Bonnet gravity: a gauge invariant study for spherical evolution

TL;DR

This paper investigates the hyperbolic nature of scalar-Gauss-Bonnet gravity during spherical evolution, revealing how physical degrees of freedom influence well-posedness and highlighting limitations of gauge-invariant methods.

Contribution

It provides a gauge-invariant analysis of hyperbolicity in scalar-Gauss-Bonnet gravity, showing how additional scalar interactions can mitigate loss of well-posedness.

Findings

Loss of hyperbolicity linked to physical degrees of freedom.

Additional scalar interactions can stabilize evolution.

Gauge-invariant approach has limitations due to field redefinitions.

Abstract

We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach of Ref.~\cite{Reall:2021voz} to track well-posedness. Our results show that loss of hyperbolicity when it occurs, is due to the behaviour of physical degrees of freedom. They provide further support to the idea that this behaviour can be tamed by additional interactions of scalar. We also point out a limitation of this gauge-invariant approach: the fact that field redefinitions can change the character of the evolution equations.