The initial value problem of scalar-tensor theories of gravity

TL;DR

This paper develops a well-posed initial value formulation for scalar-tensor theories of gravity in the Jordan frame, enabling analysis of black hole formation, scalar gravitational waves, and cosmological dynamics.

Contribution

It introduces a strongly hyperbolic 3+1 system for scalar-tensor theories, facilitating the study of their dynamical behavior and stability in various spacetime configurations.

Findings

Constructed initial data for black hole formation and scalar wave emission.

Analyzed cosmological evolution within scalar-tensor theories.

Established well-posedness of the initial value problem in the Jordan frame.

Abstract

The initial value problem of scalar-tensor theories of gravity (STT) is analyzed in the physical (Jordan) frame using a 3+1 decomposition of spacetime. A first order strongly hyperbolic system is obtained for which the well posedness of the Cauchy problem can be established. We provide two simple applications of the 3+1 system of equations: one for static and spherically symmetric spacetimes which allows the construction of unstable initial data (compact objects) for which a further black hole formation and scalar gravitational wave emission can be analyzed, and another application is for homogeneous and isotropic spacetimes that permits to study the dynamics of the Universe in the framework of STT.