Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems - Madhukrishna Chakraborty; Subenoy Chakraborty (European Physical Journal C: Particles and Fields)
Abstract The present work analyses Raychaudhuri equation (RE) in Einstein gravity for two interacting fluids. Focusing theorem, a consequence of RE, is directly related to the singularity theorems of Penrose and Hawking. In the present work, the signature of the Raychaudhuri scalar or convergence scalar has been examined for two types of interaction forms namely, (i) $$Q=H(α ρ _1+β ρ _2)$$ Q = H ( α ρ 1 + β ρ 2 ) (linear) and (ii) $$Q=\dfrac{Hξ ρ _1ρ _2}{α ρ _1+β ρ _2}$$ Q = H ξ ρ 1 ρ 2 α ρ 1 + β ρ 2 (non-linear). Finally, the phenomena of focusing of a congruence of geodesics and possible avoidance of singularity have been discussed based on the nature of the two fluids and the interaction term operating between them.