# Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects

## TL;DR

This paper investigates how tilted congruences and Palatini $f(R)$ gravity influence the development of inhomogeneities in spherical relativistic systems, revealing that these factors can suppress energy-density irregularities in regular compact objects.

## Contribution

It introduces an analysis of the combined effects of observer tilt and Palatini $f(R)$ gravity on inhomogeneity factors in relativistic models, which is a novel approach.

## Key findings

- Tilted congruences significantly alter inhomogeneity variables.
- Palatini $f(R)$ terms tend to prevent energy-density inhomogeneities.
- Homogeneity persists in conformal flat dust and perfect fluids under certain conditions.

## Abstract

The purpose of this paper is to check the impact of observer and Palatini $f(R)$ terms in the formulations of inhomogeneity factors of spherical relativistic systems. We consider Lema\^{i}tre-Tolman-Bondi dynamical model as a compact object and studied its evolution with both tilted and non-tilted observers. We performed our analysis for particular cases of fluid distribution in tilted frame and found some energy density irregularity variables. We found that these variables are drastically different from those observed by non-tilted observer. The conformal flat dust and perfect matter contents are homogeneous as long as they impregnate vacuum core. However, this restriction is relaxed, when the complexity in the fluid description is increased. The radial fluid velocity due to tilted congruences and Palatini $f(R)$ curvature terms tend to produce hindrances in the appearance of energy-density inhomogeneities in the initially regular spherical stellar populations.