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Stability criterion for white dwarfs in Palatini $f(R)$ gravity

Recent observations of several peculiar over- and under-luminous type Ia supernovae infer indirect evidence for the violation of the Chandrasekhar mass-limit by suggesting the existence of super- and sub-Chandrasekhar limiting mass white dwarfs. In an attempt to explain these phenomena in the context of general relativistic extensions, we study these objects in Palatini $f(R)$ gravity. We obtain the super- and sub-Chandrasekhar limiting masses as well as the dynamical instability criteria for white dwarfs in the given gravitational theory. We further demonstrate that the conventional positivity condition $\partial{M}/\partial{ρ_\text{c}}>0$ with $M$ being the WD's mass with central density $ρ_\text{c}$, is also a valid criterion for stability in Palatini gravity.