On the Cauchy Problem for Weyl-Geometric Scalar-Tensor Theories of Gravity

TL;DR

This paper investigates the initial value problem for Weyl-integrable scalar-tensor gravity theories, demonstrating well-posedness and geometric uniqueness, and relating findings to Brans-Dicke theory.

Contribution

It establishes the well-posedness and geometric uniqueness of the Cauchy problem in Weyl geometric scalar-tensor theories, extending understanding to vacuum solutions and connecting with Brans-Dicke models.

Findings

Cauchy problem in vacuum is well-posed.

Geometric uniqueness of solutions is proven.

Results relate to and extend Brans-Dicke theory insights.

Abstract

In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant interpretation for the theory, the Cauchy problem in vacuum is well-posed. We will analyse the global in space problem, and, furthermore, we will show that geometric uniqueness holds for the solutions. We make contact with Brans-Dicke theory, and by analysing the similarities with such models, we highlight how some of our results can be translated to this well-known context, where not all of these problems have been previously addressed.