Extending the ADM formalism to Weyl geometry

TL;DR

This paper extends the ADM formalism to Weyl geometry to facilitate quantum cosmology studies in spacetimes with Weyl structures, providing a new framework for analyzing such models.

Contribution

It introduces a (3+1)-dimensional split of Weyl spacetimes and formulates a Weyl gravity Lagrangian, extending general relativity for quantum cosmology applications.

Findings

Derived curvature tensor in Weyl geometry with spatial quantities

Formulated Weyl gravity Lagrangian compatible with ADM formalism

Established a framework for quantum cosmology in Weyl spacetimes

Abstract

In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+1)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.