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

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