(2+1)-Dimensional Gravity in Weyl Integrable Spacetime

TL;DR

This paper explores (2+1)-dimensional gravity within Weyl integrable spacetime, revealing unique features such as a Newtonian limit in any dimension and specific vacuum solutions with potential naked singularities.

Contribution

It demonstrates that Weyl integrable spacetime modifies (2+1)-dimensional gravity, providing new solutions and insights into the geometric nature of such theories.

Findings

WIST admits a Newtonian limit in any dimension.

Non-vanishing geodesic deviation in 3D pressureless fluid.

Existence of static vacuum solutions with naked singularities.

Abstract

We investigate (2+1)-dimensional gravity in a Weyl integrable spacetime (WIST). We show that, unlike general relativity, this scalar-tensor theory has a Newtonian limit for any dimension and that in three dimensions the congruence of world lines of particles of a pressureless fluid has a non-vanishing geodesic deviation. We present and discuss a class of static vacuum solutions generated by a circularly symmetric matter distribution that for certain values of the parameter w corresponds to a space-time with a naked singularity at the center of the matter distribution. We interpret all these results as being a direct consequence of the space-time geometry.