Compact Objects in EBIKK-β Gravity: Magnetars, Ergostars and Neutron Stars

This series of studies explores the behavior of compact astrophysical objects within the Entropic-Born-Infeld-Kaluza-Klein (EBIKK) framework with β-regularization. The unified model combines nonlinear electrodynamics, entropic gravity, and extra-dimensional compactification topredict:• Magnetars with ultra-strong magnetic fields (Bmax ∼ 1018 G) andmodified X-ray emission spectra• Stable ergostars - horizonless ultracompact objects with ergoregions - as alternatives to black holes• Neutron stars with regularized cores (RµνρσRµνρσ < β−1) andincreased maximum mass (∼ 2.8M⊙)Key theoretical innovations include:• β-dependent curvature bounds (β ∼ 10−56 m4)• Entropic corrections to thermodynamics• Modified equations of state at high densitiesThe model provides testable predictions for:• Gravitational wave signatures (∆ω/ω ∼ 10−6)• X-ray spectra of compact objects• Neutron star mass-radius relationsAll solutions maintain UV-completeness while reproducing known observational constraints from NICER, LIGO/Virgo, and X-ray telescopes.本系列研究探索了带β正则化的熵-玻恩-因费尔德-卡鲁扎-克莱因（Entropic-Born-Infeld-Kaluza-Klein, EBIKK）框架下的致密天体物理对象行为。该统一模型融合非线性电动力学、熵引力与额外维度紧致化理论，可得出如下预测： • 拥有超强磁场（最大磁场B_max≈10^18高斯）且X射线发射光谱发生修正的磁星 • 稳定ergostar——一类具备能层的无视界超致密天体，可作为黑洞的替代候选体 • 拥有正则化核心（黎曼曲率张量平方R_{μνρσ}R^{μνρσ} < β^{-1}）且最大质量增至约2.8倍太阳质量的中子星 该模型的核心理论创新包括： • 与β相关的曲率约束（β≈10^{-56} 米^4） • 热力学的熵修正 • 高密度条件下的修正物态方程 该模型可给出如下可检验预言： • 引力波特征信号（Δω/ω≈10^{-6}） • 致密天体的X射线光谱 • 中子星的质量-半径关系 所有求解结果均保持紫外完备性，同时可复现来自NICER、LIGO/Virgo及X射线望远镜的已知观测约束。