Covariant gravitational dynamics in 3+1+1 dimensions

Details Covariant gravitational dynamics in 3+1+1 dimensions Covariant gravitational dynamics in 3+1+1 dimensions

2009-09-02

arxiv.org/abs/0909.0490v2

Class.Quant.Grav.27:105009,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages 1 fig; significantly expanded with (a) new closure condition on the brane, (b) discussion of anisotropic brane-worlds

Scientific paper

10.1088/0264-9381/27/10/105009

We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical, gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction conditions across the brane in terms of the new variables. Then we establish a closure condition for the equations on the brane. We also establish the connection of this formalism with isotropic and anisotropic cosmological brane-worlds. Finally we derive a new brane solution in the framework of our formalism: the tidal charged Taub-NUT-(A)dS brane, which obeys the closure condition.

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