Role of Structure Scalars on the evolution of Compact Objects in Palatini $f(R)$ Gravity

TL;DR

This paper develops modified structure scalars within Palatini $f(R)$ gravity to analyze the evolution of compact objects, providing a formalism that links gravitational theory modifications with stellar structure and dynamics.

Contribution

It introduces a novel formalism for structure scalars in Palatini $f(R)$ gravity and applies it to study the evolution of compact stellar objects.

Findings

Derived scalar functions related to physical properties of fluid sources.

Analyzed the impact of modified gravity on stellar evolution.

Provided insights into structure formation in Palatini $f(R)$ gravity.

Abstract

The utmost concern of this article is the construction of modified scalar functions (structure scalars) by taking Palatini $f(R)$ gravitational theory into account. At first, a general formalism is established in which we assess gravitational stellar equations by putting into use the Palatini's technique. Later, from the perspective of tilted observer, we Lorentz boosted the components of energy-momentum tensor using relative velocity $\omega$. To examine the physical as well as mathematical aspects of the fluid source, we carry out a detailed analysis of kinematical variables by evaluating shear tensor and scalar, four-acceleration and expansion scalar. For the fluid content inside our spherical star, we inferred the mass function (geometric mass) and the active gravitational mass. Raychaudhuri equation, Bianchi identities in addition to few other equations are worked out to discern the structure formation and analyze the object's evolutionary stages. The Riemann tensor is then broken up orthogonally to set up few scalar functions connected with fundamental physical characteristics of the fluid source like energy density, effects of tidal forces and anisotropic stresses etc.