Herrera Complexity and Shadows of Spherically Symmetric Compact Objects

TL;DR

This paper explores how the complexity factor of spherically symmetric compact objects influences the formation and stability of photon spheres and shadows, linking geometric and matter properties with observable astrophysical phenomena.

Contribution

It introduces the concept of complexity factor as a classification tool for gravitating objects and investigates its impact on photon ring formation and stability.

Findings

Zero complexity systems are significant for photon ring formation.

Complexity correlates with shadow and photon ring stability.

Provides a theoretical framework connecting matter inhomogeneity with observable features.

Abstract

In this work we investigate the effect of complexity factor on the formation of photon spheres for spherically symmetric compact objects. The complexity factor obtained from the orthogonal splitting of the Riemann curvature tensor connects the geometric attributes of a compact spherically symmetric gravitating object with its matter inhomogeneity and pressure anisotropy via a scalar term. The novelty of the complexity factor is the inherent simple definition that identifies the evolution of matter tensors inside a given region of space-time. Such identification helps to obtain an equivalence class of gravitating compact objects based on their degree of complexity with zero complexity identified as the simplest system. On the other hand shadows and photon rings have become essential for identifying compact regions of space time characterised by massive gravity. Advanced observational data analysis tools augments the hope for identification of exotic gravitational objects, like the so called ``black hole mimickers" and may serve as testing ground for other gravity theories. In this context we explore how complexity of compact objects (a fundamentally theoretical classification) is connected to the photon ring (an astrophysical observable in the universe) and its stability. We consider zero complexity systems and discuss its significance with respect to (wrt) formation of photon rings and hence shadows.