强曲率奇点穿孔邻域中的精确结果
Exact results in a punctured neighborhood of a strong curvature singularity
AI总结：
通过构建强曲率奇点时空模型，证明其中静电场在奇点穿孔邻域有界，为穿越奇点信号传播研究开辟新途径。
摘要：
通过构建一个具有强曲率奇点的时空模型，在该模型中因果测地线是完备的，但更一般的因果曲线并不完备，我们明确表明，在该曲率奇点的每个开放穿孔邻域上，某些静电场构型是有界的。我们的计算使用了Plebanski和Tamm提供的类比引力描述，根据该描述，在一般弯曲背景上电磁场的表征等价于在平坦空间中求解麦克斯韦方程，其中物质内容满足某些非平凡的构成关系。电场在接近可被视为最坏可想象物理条件时的正则性，为进一步研究穿越时空奇点传播信号的可行性打开了大门。
英文摘要：
By constructing a model of spacetime having a strong curvature singularity in which causal geodesics are complete, but more generic causal curves are not, we explicitly show that some electrostatic field configurations on that background are bounded on every open punctured neighborhood of the curvature singularity. Our calculations are performed using the analog gravity description provided by Plebanski and Tamm, according to which the characterization of the electromagnetic field on a generic curved background is equivalent to solving Maxwell's equations in flat space with a matter content verifying certain nontrivial constitutive relations. The regularity of the electric field as it approaches what could be considered the worst conceivable physical condition, opens the door to further investigation into the possibility of propagating signals capable of crossing a spacetime singularity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
