Space-time singularities in Weyl manifolds

TL;DR

This paper extends a key singularity theorem from general relativity to Weyl integrable space-times within scalar-tensor gravity theories, using an invariant formalism to ensure frame independence.

Contribution

It introduces a generalized singularity theorem applicable to Weyl manifolds with scalar fields, broadening the scope of classical results in gravitational physics.

Findings

The theorem applies to scalar-tensor theories with Weyl geometry.

It demonstrates the conditions under which space-time singularities occur in these theories.

The formalism remains invariant under frame transformations.

Abstract

We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time (WIST). We adopt an invariant formalism, so that the extended version of theorem does not depend on a particular frame.