The Aichmayr Metric: A Curvature-Regularized Schwarzschild-Type Spacetime

We introduce a curvature-regularized Schwarzschild-type spacetime constructed entirely within classical General Relativity. The metric modifies the effective mass contribution through an exponential damping factor, introducing a characteristic length scale that suppresses curvature divergences at small radii while preserving the asymptotic Schwarzschild limit. We analyze horizon structure, curvature invariants, gravitational time dilation, and radial timelike geodesics, demonstrating that all physical quantities remain finite throughout the spacetime. An auxiliary scalar ordering field φ(t,r) is introduced as a diagnostic tool to visualize the transition between weak-field and strong-field regimes without acting as a dynamical source. The construction avoids exotic matter, higher-order curvature corrections, or modifications of the Einstein field equations, providing a minimal and geometrically transparent realization of a regular black hole spacetime.我们提出了一种完全基于经典广义相对论（General Relativity）构建的曲率正则化史瓦西类时空（Schwarzschild-type spacetime）。 该度规（metric）通过指数阻尼因子修正有效质量贡献，引入特征长度尺度，可在小半径区域抑制曲率发散，同时保留渐近史瓦西极限。 我们对视界结构、曲率不变量、引力时间膨胀以及径向类时测地线展开分析，证明该时空中所有物理量在全域均保持有限。 我们引入辅助标量序场φ(t,r)作为诊断工具，用于可视化弱场与强场区域间的过渡过程，且该场并不充当动力学源。 该构建方案规避了奇异物质、高阶曲率修正或对爱因斯坦场方程（Einstein field equations）的修改，为正则黑洞时空提供了一种极简且几何直观的实现形式。