Inhomogeneous spacetimes in Weyl integrable geometry with matter source

TL;DR

This paper explores inhomogeneous solutions in Weyl Integrable gravity with matter, explicitly deriving Szekeres spacetimes and analyzing their dynamics, revealing attractor behaviors similar to those in General Relativity.

Contribution

It provides the first explicit derivation of Szekeres solutions in Weyl Integrable theory and analyzes their dynamical properties and attractors.

Findings

Szekeres spacetimes are solutions in Weyl Integrable theory.

Only isotropic solutions include LTB spacetimes.

Kasner and Milne universes appear as attractors.

Abstract

We investigate the existence of inhomogeneous exact solutions in Weyl Integrable theory with a matter source. In particular, we consider the existence of a dust fluid source while for the underlying geometry we assume a line element which belongs to the family of silent universes. We solve explicitly the field equations and we find the Szekeres spacetimes in Weyl Integrable theory. We show that only the isotropic family can describe inhomogeneous solutions where the LTB spacetimes are included. A detailed analysis of the dynamics of the field equations is given where the past and future attractors are determined. It is interesting that the Kasner spacetimes can be seen as past attractors for the gravitation models, while the unique future attractor describes the Milne universe similar with the behaviour of the gravitational model in the case of General Relativity.