Rotation-Induced Effective Anisotropy in White Dwarfs as a Newtonian Benchmark with Relativistic Scale Assessment

We develop a one-dimensional Newtonian reduction for uniformly rotating cold white dwarfs in which the angle-averaged centrifugal support is represented by an effective anisotropic term. From the stationary Euler equation, using $⟨{\sin }^2\theta ⟩=2\mathrm{/}3$, the rotational contribution becomes ${\mathrm{\Delta }}_{\mathrm{r}\mathrm{o}\mathrm{t}}(r)=\frac{1}{3}\rho (r){\mathrm{\Omega }}^2{r}^2\mathrm{.}$ The mapping keeps the spin frequency explicit while preserving a one-dimensional hydrostatic system. With the Chandrasekhar degenerate-electron equation of state, we compute sequences over ${\rho }_c\in [{10}^6,{10}^{11}]\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$ for rotation proxies $f=\mathrm{\Omega }\mathrm{/}{\mathrm{\Omega }}_{K,0}({\rho }_c)\le 0.35$. The high-density readout shows monotonic increases of mass and radius with $f$, with a percent-level mass shift for the largest retained proxy. Applicability is checked on the rotating configurations through sub-Keplerian diagnostics and the bulk-interior measure ${\mathcal{A}}_{{10}^{-2}}$. We further compare the reduced rotational correction with an auxiliary quasi-two-dimensional reconstruction and a static isotropic Tolman–Oppenheimer–Volkoff reference sequence. These scale checks show that the reduced model remains useful for controlled trend-level surveys in the slow-rotation regime, while rotational and static relativistic corrections can both become percent-level effects at high central density. The construction provides a transparent Newtonian benchmark for future axisymmetric and relativistic rotating white-dwarf calculations.