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

Abstract

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 \(\langle\sin^2θ\rangle=2/3\), the rotational contribution becomes ${\Delta }_{\mathrm{rot}}(r)=\frac{1}{3}\rho (r){\Omega }^2{r}^2.$ 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 \(ρ_c\in[10^6,10^{11}]~{\rm g\,cm^{-3}}\) for rotation proxies \(f=Ω/Ω_{K,0}(ρ_c)\leq0.35\). 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.

35 pages, 14 figures. Substantially revised version with relativistic scale assessment, updated applicability diagnostics, a quasi-two-dimensional consistency check, revised title, and updated author list