Torsion Corrections in Brane World Gravity

Abstract

In the frame of brane world theory the effects of torsion fields are examined. Considering a five dimensional Non-Riemannian bulk with a noncompact extra dimension, we derive the modified Einstein field equations in a four dimensional (3-brane) arbitrary manifold embedded in this bulk. The necessary matching conditions are investigated assuming that the torsion in the bulk is continuous. In this context the extrinsic curvature is connected to the matter content restricted to the brane and the torsion components of the bulk. As a final result we observe that the corrections -due to torsion fields -in the modified field equations depend crucially on the embedding that is taken. Therefore, by considering a simple embedding, we develop a cosmological model that describes a flat FLRW embedded in a 5-dimensional de Sitter (or Anti de Sitter) spacetime, where a 5-dimensional cosmological constant emerges from the torsion components of the bulk.

Solutions on a brane in a bulk spacetime with Kalb–Ramond field

“…Derivation of effective field equation on a brane embeddded in a bulk is a subject of considerable interest [31][32][33][34][35]. While there have been numerous work on this with linear or higher curvature terms in the bulk, the role of antisymmetric tensor fields in the bulk has not been explored in great detail so far [39,41,42,45]. The antisymmetric tensor field can either acts as an external gauge field or equivalently can be interpreted as spacetime torsion which has the potential to change the scenario significantly.…”

“…In this work we start with a bulk spacetime endowed with KR field (such a scenario is phenomenologically quiet important, see [43,44]). We show that the effective gravitational field equation on the brane provides valuable insight to the nature of the gravitational field equations which are modified by the inclusion of KR field in the bulk [45][46][47][48][49][50]. This idea assumes special significance from the point of view of different extra dimensional models.…”

Revisiting Effective Einstein Equations on a 3-Brane in the Presence of Torsion

“…Next, assuming TAB = 0, we calculate the divergence of the effective equation (47). Contracting the 4-dimensional Bianchi identities (7) twice…”

“…Then, based on it, they obtained the projected effective Einstein equations in a 4-dimensional arbitrary manifold embedded in a 5-dimensional Riemann-Cartan manifold, different from [5]. Maier et al [5] (see also [7]) assumed the torsion in the bulk to be continuous across the brane allowing just the first derivatives appearing in the effective field equations on the 3-brane to be discontinuous, similar to the familiar assumptions on the metric. We know however, that the corresponding assumptions for the metric in Riemannian spacetimes can be made without loss of generality due to the freedom of the choice of the coordinates, which leads to the so-called admissible coordinates.…”