Hyperbolicity of scalar-tensor theories of gravity

TL;DR

This paper develops two strongly hyperbolic formulations of scalar-tensor gravity theories in the Jordan frame, demonstrating that these formulations have a well-posed Cauchy problem, which is crucial for numerical simulations.

Contribution

It introduces two new first-order strongly hyperbolic formulations of scalar-tensor theories with nonminimal couplings, extending the mathematical understanding of their well-posedness.

Findings

Both formulations are strongly hyperbolic.

The scalar-tensor theory has a well-posed Cauchy problem in the Jordan frame.

Abstract

Two first order strongly hyperbolic formulations of scalar-tensor theories of gravity (STT) allowing nonminimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the scalar-tensor theory is proposed for the analysis. This study confirms that the scalar-tensor theory posses a well posed Cauchy problem even when formulated in the Jordan frame.