White Dwarf Stellar Structure from Effective Polymer Geometry in Loop Quantum Gravity

We construct an effective Tolman Oppenheimer Volkoff system for cold carbon white dwarfs using the areal radius form of a polymer metric sector motivated by loop quantum gravity. The two asymptotic mass parameters of the geometry are retained in the stellar prescription through $M_B\rightarrow m(R)$ and $M_W=\eta m(R)$, while the polymer amplitude is controlled by $A_\lambda$. The matter sector is kept fixed and is described by the Chandrasekhar equation of state and by the same carbon model with the Coulomb lattice correction. The resulting equations recover the general relativistic TOV system and the symmetric polymer limit. For the undeformed sequences we obtain $M_{\max}=1.4166\,M_\odot$ for the Chandrasekhar model and $M_{\max}=1.3850\,M_\odot$ when the lattice correction is included. Turning on $A_\lambda$ shifts the massive part of the equilibrium sequence upward without stiffening the equation of state, reaching $M_{\max}=1.7125\,M_\odot$ and $1.6907\,M_\odot$ at $A_\lambda=100$ for the two matter models. These configurations remain within the matter domain imposed by the inverse beta decay boundary used in the scan. The asymmetric ratio $\eta=M_W/M_B$ changes the metric function near the polymer transition region, but its effect on white dwarf observables is small: across the selected configurations, $M_{\max}$ changes by less than $0.1\%$ and the corresponding radius by less than $0.33\%$. The calculation therefore identifies $A_\lambda$ as the parameter controlling the super Chandrasekhar displacement of the mass radius relation, while $\eta$ acts mainly as a geometric asymmetry parameter in the low compactness regime probed by white dwarfs.