(2+1)-dimensional gravity in Weyl integrable spacetime

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 n 3 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 ω 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.

Einstein-aether theory in Weyl integrable geometry

“…The energy momentum tensorT ae μν is derived by variation with respect to to the coformal metricg μν , because the energy momentum tensor to be defined in the Weyl integrable manifold, see also the discussion in [41,49],…”

Inhomogeneous spacetimes in Weyl integrable geometry with matter source

“…[44], while higher-or lower-dimensional gravitational models were studied in Refs. [40,42,43]. In Ref.…”

Integrability and cosmological solutions in Einstein-æther-Weyl theory

“…In Weyl integrable theory the geometry is supported by the metric tensor and a connection structure which differs from the conformally equivalent metric by a scalar field [38,39]. Cosmological and gravitational applications of the Weyl geometry can be found for instance in [48][49][50][51][52][53][54][55][56][57]. The novelty of the Weyl geometry is that the scalar field in the gravitational Action integral is introduced by the geometry.…”