The Schönberg–Chandrasekhar limit in presence of small anisotropy and modified gravity

The Sch\"{o}nberg-Chandrasekhar limit in post main sequence evolution for stars of masses the range $1.4\lesssim M/M_{\odot}\lesssim 6$ gives maximum pressure that stellar core can withstand, once central hydrogen is exhausted. It usually expressed as a quadratic function $1/\alpha$, with $\alpha$ being ratio mean molecular weight to envelope. Here, we revisit this scenarios where balance equation interior may be modified, and presence small anisotropy, might arise due several physical phenomena. Using numerical analysis, derive three parameter dependent master formula limit, discuss various consequences. As byproduct, limiting case our formula, find standard Newtonian framework, best fitted by polynomial linear, rather than quadratic, lowest order $1/\alpha$.