Complexity and structure scalars of Type II matter fields

TL;DR

This paper uses a covariant approach to analyze the complexity of Type II matter fields in generalized Vaidya spacetime, revealing how structure scalars relate to matter variables and their evolution.

Contribution

It introduces a detailed analysis of structure scalars for Type II matter fields, including the complexity factor and its relation to spacetime and matter properties.

Findings

Vanishing complexity class of spacetimes identified

Pure Type II Vaidya spacetime has negative complexity

Propagation equations of structure scalars derived

Abstract

A general semi-tetrad covariant approach is adopted to analyse the structure scalars of a Type II fluid in generalized Vaidya spacetime. The relationship between the $1+1+2$ covariant quantities and the structure scalars are obtained. We calculate the complexity factor in terms of the Misner-Sharp mass and the matter variables to obtain a non-trivial class of spacetimes with vanishing complexity. Also the Vaidya spacetime with pure Type II matter field has negative complexity. The differences between the complexity of Type I and Type II matter fields are highlighted. We compute the propagation and evolution equations of the structure scalars, showcasing their interdependency through the kinematical variables. The causal wave equation of the Gaussian curvature of the 2-shell and its dependence on the structure scalars are also studied.