Complexity of Dynamical Sphere in Self-interacting Brans-Dicke Gravity

TL;DR

This paper develops a measure of complexity for dynamic spherical systems in self-interacting Brans-Dicke gravity, analyzing how scalar fields influence their evolution and deviation from simple models.

Contribution

It introduces a new definition of complexity based on structure scalars in Brans-Dicke gravity and explores the effects of scalar fields on system evolution.

Findings

Homologous models follow the simplest evolution mode.

Scalar fields increase the complexity of the system.

Complexity grows when the system deviates from initial zero-complexity state.

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.