Complexity and Structure Scalars of Generalized Vaidya Spacetime

We study gravitational complexity in the framework of Generalized Vaidya geometry for the first time. Adopting a general semi-tetrad covariant approach, we find the structure scalars of a Type II fluid in this spacetime and establish the relationship between the 1+1+2 covariant quantities and these structure scalars. By calculating the complexity factor in terms of the Misner–Sharp mass and the matter variables, we obtain a non-trivial class of spacetimes with vanishing complexity. Furthermore, we show that the Vaidya spacetime with a pure Type II matter field yields a negative complexity factor, highlighting the fundamental difference between the complexity of Type I and Type II matter fields. We also compute the propagation and evolution equations of the structure scalars to showcase their interdependency through the kinematical variables. Finally, we study the wave equation of the gravitational mass of the 2-shell and analyze its dependence on these structure scalars.