Covariant gravitational dynamics in 3+1+1 dimensions

TL;DR

This paper introduces a covariant 3+1+1 formalism for analyzing gravitational dynamics in brane-world scenarios, providing new equations, junction conditions, and a novel brane solution with cosmological applications.

Contribution

The paper develops a new covariant formalism for 3+1+1 dimensions, deriving evolution equations, junction conditions, and a novel tidal charged Taub-NUT-(A)dS brane solution.

Findings

Derived evolution and constraint equations on and off the brane.

Established junction and closure conditions for the formalism.

Constructed a new tidal charged Taub-NUT-(A)dS brane solution.

Abstract

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.