Braneworld Remarks in Riemann-Cartan Manifolds

Details Braneworld Remarks in Riemann-Cartan Manifolds Braneworld Remarks in Riemann-Cartan Manifolds

2008-04-27

arxiv.org/abs/0804.4261v4

Class.Quant.Grav. 26 (2009) 055007; 26 (2009) 179801

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages. A corrected misprint in def.(18), and the respective terms in Eqs.(20-23). All physical consequences remain unchanged

Scientific paper

10.1088/0264-9381/26/5/055007

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.

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