发表机构
San Diego State University; University of California San Diego; Universidad Nacional Autónoma de México; Frankfurt Institute for Advanced Studies (FIAS), J. W. von Goethe Universität; International Center for Relativistic Astrophysics Network (ICRANet); Universidade Federal do Rio Grande do Sul（圣地亚哥州立大学; 加州大学圣地亚哥分校; 墨西哥国立自治大学; 法兰克福高等研究院，约翰·沃尔夫冈·冯·歌德大学; 国际相对论天体物理网络中心; 南里奥格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对广义相对论在高曲率下的奇点问题，提出伪复广义相对论通过引入辅助场和lapse下界，结合正则条件消除Schwarzschild型发散，实现曲率正则化。
AI 中文摘要
经典时空在任意高曲率下是否仍然定义良好是一个核心问题。在广义相对论中，奇点标志着经典描述的失效，这促使人们对时空的短距离结构进行修正。伪复广义相对论（pcGR）将时空几何扩展到伪复坐标，自然引入了两个度量扇区：物理度量g{\mu}{\nu}和辅助场f{\mu}{\nu}。伪虚分量的大小定义了不变加速度标度a0，这是伪复结构的直接结果。同时性条件要求两个幂等扇区独立满足伪复爱因斯坦方程，从而代数地确定辅助场，不引入新的传播自由度，并为 lapse 函数设置了一个下界，从而正则化曲率。正则化是通过 lapse 间隙条件 e{\nu}(r) > a0 与面积半径原点处的正则条件 B(0) = 1 和 B'(0) = 0 的联合作用实现的，其中 lapse 间隙条件确保径向度量分量保持非退化，而正则条件则自然地从伪复几何中涌现。这些条件共同消除了 Schwarzschild 型曲率发散，而非间隙条件单独作用。
英文摘要
Whether classical spacetime remains welldefined at arbitrarily high curvature is a central question. In general relativity, singularities signal the breakdown of the classical description, motivating modifications of spacetime's short-distance structure. Pseudocomplex general relativity (pcGR) extends spacetime geometry to pseudo-complex coordinates, naturally introducing two metric sectors, the physical metric gμν and an auxiliary field fμν. The magnitude of the pseudo imaginary component defines the invariant acceleration scale a0, a direct consequence of the pseudo-complex structure. The simultaneity condition, requiring both idempotent sectors to satisfy the pseudo-complex Einstein equations independently, fixes the auxiliary field algebraically, with no new propagating degrees of freedom, and sets a lower bound on the lapse that regularizes curvature. The regularization is achieved through the combined effect of the lapse-gap condition eν(r) gt. a0, which ensures the radial metric component remains nondegenerate, together with the regularity conditions at the areal-radius origin, B(0) = 1 and B'(0) = 0, which emerge naturally from the pseudo-complex geometry. These conditions jointly eliminate the Schwarzschildtype curvature divergence, rather than the gap condition acting alone.
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