Possible Generalizations within Braneworld Scenarios: Torsion fields

TL;DR

This paper explores how torsion fields influence braneworld scenarios, analyzing their effects on Einstein equations, black hole properties, and potential measurable phenomena like quasar luminosity, within a 5D Riemann-Cartan framework.

Contribution

It extends the formalism of braneworld models to include torsion effects, revealing their impact on effective Einstein equations and potential observational signatures.

Findings

Torsion does not modify Israel-Darmois matching conditions.

Torsion significantly alters the effective Einstein equations on the brane.

Bulk torsion effects are generally suppressed by the internal space volume.

Abstract

In this Chapter we introduce the aspects in which torsion can influence the formalism of braneworld scenarios in general, and also how it is possible to measure such kind of effects, namely, for instance, the blackstring transverse area corrections and variation of quasar luminosity due to those corrections. We analyze the projected effective Einstein equation in a 4-dimensional arbitrary manifold embedded in a 5-dimensional Riemann-Cartan manifold. The Israel-Darmois matching conditions are investigated, in the context where the torsion discontinuity is orthogonal to the brane. Unexpectedly, the presence of torsion terms in the connection does not modify such conditions whatsoever, despite of the modification in the extrinsic curvature and in the connection. Then, by imposing the Z2-symmetry, the Einstein equation obtained via Gauss-Codazzi formalism is extended, in order to now encompass the torsion terms. We also show that the factors involving contorsion change drastically the effective Einstein equation on the brane, as well as the effective cosmological constant. Also, we present gravitational aspects of braneworld models endowed with torsion terms both in the bulk and on the brane. In order to investigate a conceivable and measurable gravitational effect, arising genuinely from bulk torsion terms, we analyze the variation in the black hole area by the presence of torsion. Furthermore, we extend the well known results about consistency conditions in a framework that incorporates brane torsion terms. It is shown, in a rough estimate, that the resulting effects are generally suppressed by the internal space volume.