Complexity of dynamical sphere in self-interacting Brans–Dicke gravity

Abstract

Abstract This paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans–Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic pressure and massive scalar field. For this purpose, we formulate structure scalars by orthogonally splitting the Riemann tensor. We show that self-gravitating models collapsing homologously follow the simplest mode of evolution. Furthermore, we demonstrate the effect of scalar field on the complexity and evolution of non-dissipative as well as dissipative systems. The criteria under which the system deviates from the initial state of zero complexity is also discussed. It is concluded that complexity of the sphere increases in self-interacting Brans–Dicke gravity because the homologous model is not shear-free.