AI 中文总结
该研究为黑洞种子的纽曼 - 贾尼斯型变形构建阻碍与剩余完备理论，将算法视为离壳映射，用张量编码失败并分解剩余量。通过线性可解性问题判断，以史瓦西为例说明框架，用可计算准则取代对复化规则的搜索。
AI 中文摘要
我们为黑洞种子的纽曼 - 贾尼斯型变形制定了一种阻碍与剩余完备理论，其中纽曼 - 贾尼斯型包括原始的复坐标纽曼 - 贾尼斯算法以及诸如非复化变体等修改后的处方。纽曼 - 贾尼斯算法被视为从静态种子到稳态轴对称试验几何的离壳映射，而非解生成定理。其失败由纽曼 - 贾尼斯阻碍张量编码，该张量定义为将试验构型代入预期场方程后得到的剩余量。我们将此剩余量分解为动力学、几何/坐标可容许性和源保持通道，将场方程失败与循环性、博伊尔 - 林德奎斯特可积性、应力张量类型、状态方程保持以及物质模型可实现性区分开来。当阻碍不为零时，剩余完备性询问度规和物质场的最小修正是否能消除它。在旋转参数的主导非零阶，这成为一个线性可解性问题：阻碍必须位于受边界和源区约束的规范固定完备算子的像中，而余核条件在所选假设类中给出一个不可行准则。我们用真空广义相对论中的史瓦西例子说明了该框架。使用不同于生成克尔度规的一种ONJA型复化，我们得到一个非克尔旋转试验度规并计算其阻碍。该例子给出\(n_* = 2\)和\(\ell_* = 0\)，在同一阶有一个额外的四极分量，并展示了如何通过恢复克尔复化的最小偶宇称修正消除主导剩余量。该框架用成功、完备或阻碍的可计算准则取代了对正确复化规则的搜索。
英文摘要
We formulate an obstruction and residual-completion theory for Newman-Janis-type deformations of black hole seeds, where Newman-Janis-type includes both the original complex-coordinate Newman-Janis algorithm and modified prescriptions such as non-complexification variants. The Newman-Janis algorithm is treated as an off-shell map from a static seed to a stationary-axisymmetric trial geometry, rather than as a solution-generating theorem. Its failure is encoded in a Newman-Janis obstruction tensor, defined as the residual obtained after substituting the trial configuration into the intended field equations. We decompose this residual into dynamical, geometrical/coordinate-admissibility, and source-preservation channels, separating field-equation failure from circularity, Boyer-Lindquist integrability, stress-tensor type, equation-of-state preservation, and matter-model realizability. When the obstruction is nonzero, residual completion asks whether a minimal correction of the metric and matter fields can cancel it. At leading nonzero order in the rotation parameter, this becomes a linear solvability problem: the obstruction must lie in the image of a gauge-fixed completion operator subject to boundary and source-sector constraints, while the cokernel condition gives a no-go criterion in the chosen ansatz class. We illustrate the framework with a Schwarzschild example in vacuum GR. Using an ONJA-type complexification different from the Kerr-generating one, we obtain a non-Kerr rotating trial metric and compute its obstruction. The example gives $n_\star=2$ and $\ell_\star=0$, with an additional quadrupolar component at the same order, and shows how the leading residual is removed by the minimal even-parity correction restoring the Kerr complexification. The framework replaces the search for the correct complexification rule with computable criteria for success, completion, or obstruction.
Comments25 pages. Accepted for publication in EPJC
Journal refEur. Phys. J. C (2026) 86:926
DOI：10.1140/epjc/s10052-026-16158-1
