Self similar collapse and the Raychaudhuri equation

Abstract

The role of the Raychaudhuri equation in studying gravitational collapse is discussed. A self-similar distribution of a scalar field along with an imperfect fluid in a conformally flat spacetime is considered for the purpose. The general focusing condition is found out and verified against the available exact solutions. The connection between the Raychaudhuri equation and the critical phenomena is also explored.

Role of a magnetic field in the context of inhomogeneous gravitational collapse

“…So, we can see that the Raychaudhuri equation leads to important general conclusions even without any explicit solution of the field equations. This is a useful aspect of this Raychaudhuri equation based approach (for example see [10,12,31]).…”

“…The first one is ξ → ∞ which will give us an idea about the formation of a central singularity (another limit, t → ∞ is inconsequential). It is clear from equations (31), (32) and ( 33) that R αβ u α u β , ∇ α a α ≫ σ αβ σ αβ in this limit and we can ignore the effect of shear. Thus, to avoid formation of a central singularity due to collapse we need,…”

“…The idea of applying Raychaudhuri's equation in collapsing situations was introduced by Germani and Tsagas in the context of magnetized Tolman-Bondi collapse [8]. Later this technique has been applied in a few other models of gravitational collapse [9,10,11,12,31].…”