Weak-field limit of $f(R)$ gravity to unify peculiar white dwarfs

TL;DR

This paper derives the weak-field limit of $f(R)$ gravity and uses it to model the structure of peculiar white dwarfs with masses beyond the Chandrasekhar limit, explaining under- and over-luminous supernovae.

Contribution

It provides a derivation of the weak-field limit of $f(R)$ gravity and applies it to explain peculiar white dwarf structures with a single model parameter.

Findings

Derived the higher-order correction to the Poisson equation from $f(R)$ gravity.

Modeled sub- and super-Chandrasekhar white dwarfs using the weak-field limit.

Explained the mass limits of white dwarfs in the context of modified gravity.

Abstract

In recent years, the idea of sub- and super-Chandrasekhar limiting mass white dwarfs (WDs), which are potential candidates to produce under- and over-luminous type Ia supernovae, respectively, has been a key interest in the scientific community. Although researchers have proposed different models to explain these peculiar objects, modified theories of Einstein's gravity, particularly $f(R)$ gravity with $R$ being the scalar curvature, seems to be one of the finest choices to explain both the regimes of these peculiar WDs. It was already shown that considering higher-order corrections to the Starobinsky model with two parameters, the structure of sub- and super-Chandrasekhar progenitor WDs can be explained self consistently. It is also well-known that WDs can be considered Newtonian objects because of their large size. In this paper, we derive the weak-field limit of $f(R)$ gravity, which turns out to be the higher-order correction to the Poisson equation. Later, we use this equation to obtain the structures of sub- and super-Chandrasekhar limiting mass WDs at various central densities incorporating just one model parameter.