AI 中文总结
该研究针对正则黑洞，推导球对称引力场方程的局域一致性宇称选择规则，证实静态解曲率正则性不足以保证动力学一致性，确定了满足规则的理论类别及相关条件。
AI 中文摘要
正则黑洞度通常在运动学框架下研究，但有限曲率的静态核心无法保证基础理论能一致地演化穿过正则中心的普通物质。我们在球对称下最一般的基于作用量、恒等守恒的二阶引力场方程类别中，推导出一个必要的局域一致性条件。正则性要求定义该理论的两个函数在带符号径向坐标反转时具有相反宇称，同时满足额外的中心正则性和非退化条件。在可积领域，该准则等价于要求广义Misner–Sharp–Hernandez质量在中心处为奇函数、在中心处三次方消失且不含点质量贡献。对于从静态单参数真空族重构的理论，该条件变为半径与质量同时反转下的协变。与Hayward和Dymnikova几何相关的理论满足该选择规则，而Bardeen理论不满足，表明静态解的曲率正则性不足以保证与普通物质的动力学一致性。我们还刻画了包含类Hayward黑洞（带有de Sitter核心）的无限类可容许理论。该选择规则为旨在描述正则坍缩的理论提供必要条件，但本身不能确立适定性或保证非奇异终点。
英文摘要
Regular black hole metrics are usually studied kinematically, but a finite-curvature static core does not guarantee that the underlying theory can consistently evolve generic matter through a regular center. We derive a necessary local consistency condition within the most general class of action-based, identically conserved, second-order gravitational field equations in spherical symmetry. Regularity requires that the two functions defining the theory have opposite parities under reversal of the signed radial coordinate, together with additional center-regularity and nondegeneracy conditions. In the integrable sector, this criterion is equivalent to requiring the generalized Misner--Sharp--Hernandez mass to be odd across the center, to vanish cubically there, and to contain no point-mass contribution. For theories reconstructed from static one-parameter vacuum families, the condition becomes covariance under simultaneous reversal of radius and mass. The theories associated with the Hayward and Dymnikova geometries satisfy this selection rule. In contrast, the Bardeen theory does not, demonstrating that curvature regularity of a static solution is insufficient for dynamical consistency with generic matter. We also characterize an infinite class of admissible theories containing Hayward-like black holes with de Sitter cores. The selection rule provides a necessary condition for theories intended to describe regular collapse, but does not by itself establish well-posedness or guarantee a nonsingular endpoint.
