强偏转极限下Z₂对称虫洞喉处边缘不稳定光子球内外的引力透镜效应
Gravitational lensing outside and inside of a marginally unstable photon sphere at a $Z_2$-symmetric wormhole throat in strong deflection limits
AI总结：
本文研究Z₂对称虫洞喉处边缘不稳定光子球内外的引力透镜效应，发现其偏折角呈幂次发散，修正了相关幂次发散项系数，得到强偏转极限下该类虫洞偏折角的普适性质。
AI中文摘要：
光线的偏折角在黑洞光子球内外附近会对数发散，且可能被未来近地空间观测在黑洞阴影中探测到。本文研究了一类常用虫洞或简单虫洞（常被事件视界望远镜（Event Horizon Telescope）合作组研究）的喉处光子球附近光线的偏折角，发现其并非对数发散，而是幂次发散，原因在于该类虫洞在Z₂对称虫洞喉处具有边缘不稳定光子球，且该虫洞具备特殊性质而非普通简单性质。本文在强偏转极限下，数值研究了Z₂对称虫洞喉处边缘不稳定光子球内外、偏折角呈幂次发散的光线引力透镜效应，将数值方法应用于常用的简单虫洞时空、Damour-Solodukhin虫洞时空及Simpson-Visser黑洞反弹时空。数值结果表明，强偏转极限下Z₂对称虫洞喉处边缘不稳定光子球的偏折角具有普适性质，与喉外边缘不稳定光子球弯曲光线的偏折角（幂次不同）类似；此外，本文采用作者及他人研究的半解析方法，修正了Z₂对称虫洞喉处边缘不稳定光子球外附近弯曲光线偏折角的幂次发散项系数。
英文摘要：
The deflection angles of rays diverge logarithmically near outside and inside of a photon sphere and they could be detected by near-future space observations on black hole shadows. We show that the deflection angles of the rays near a photon sphere at the throat of an example among some commonly used types of wormholes or one of the simple wormholes, which is often studied by the Event Horizon Telescope collaborations, does diverge not logarithmically but in power. This is because it has a marginally unstable photon sphere at a $Z_2$-symmetric wormhole throat and the wormhole has not a common nor simple but a special property. We investigate numerically gravitational lensing of rays with the deflection angles diverging in power outside and inside of a marginally unstable photon sphere at $Z_2$-symmetric wormhole throat in strong deflection limits. We apply our numerical method to the commonly-used simple wormhole spacetime, a Damour-Solodukhin wormhole spacetime, and a Simpson-Visser black-bounce spacetime. Our numerical results imply universal property of the deflection angle by the marginally unstable photon sphere on $Z_2$-symmetric wormhole throat in the strong deflection limits as similar to the deflection angles of ray bent by a marginally unstable photon sphere off a throat in the strong deflection limits which have a different power. We also correct the coefficients of power-divergent terms of deflection angles of the rays bent nearly outside of the marginally unstable photon sphere at the $Z_2$-symmetric wormhole throat in a semi-analytic approach investigated by the author and others.
