Curvature invariants for the Bianchi IX spacetime filled with tilted dust

Abstract

We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime close to the singularity for which we provide heuristic considerations supported by numerical simulations. The present paper is an extension of our earlier publication [1].

Generic instability of the dynamics underlying the Belinski–Khalatnikov–Lifshitz scenario

“…The evolution presented two recent papers [18,19] are just numerical simulations of the related dynamics in the Bianchi IX model case.…”

Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario

“…Our special monotonic solution ( 7) is generically unstable against perturbations of the initial data (15).…”

“…In this paper we present an analytical solution to that prototype, to our best knowledge, unknown before. The evolution presented in the two recent papers [14,15] are just numerical simulations of the related dynamics in the Bianchi IX model case.…”

“…In that limit the directional scale factors go to zero so that the space volume V goes to zero as well. The latter means (see [14,15] for more details) that the system approaches the gravitational singularity.…”

“…The manifold M defined by {K 1 , K 2 , K 3 , ϕ 1 , ϕ 2 } is a submanifold of R 5 . The solution defined by ( 16) and ( 19) corresponds to the choice of the set of the initial data N that is a small neighborhood of the initial data (15). N is a submanifold of R 5 as (15) defines five independent constants due to the constraint (2).…”