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

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.

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• A generalized Weyl structure with arbitrary non-metricity
• Inhomogeneous spacetimes in Weyl integrable geometry with matter source
• Double layers in Weyl geometry and some physical implications