Possible Generalizations WITHIN BRANEWORLD SCENARIOS: Torsion Fields

摘要

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 Z_2-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. This formalism provides manageable models and their possible ramifications into some aspects of gravity in this context, and cognizable corrections and physical effects as well. The torsion influences the braneworld scenario and we can check it by developing the bulk metric Taylor expansion around the brane, which brings corrections in the blackstring transverse area. This generalization is presented in order to better probe braneworld properties in a Riemann-Cartan framework, and it is also shown how the factors involving contorsion change the effective Einstein equation on the brane, the effective cosmological constant, and their consequence in a Taylor expansion of the bulk metric around the brane.