Ellis虫洞上的带电Klein-Gordon模式：磁约束与条件Heun可解性
Charged Klein-Gordon modes on an Ellis wormhole: magnetic confinement and conditional Heun solvability
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中文总结 AI 辅助
本研究在(2+1)维Ellis虫洞上研究带电Klein-Gordon模式，发现磁场导致径向约束，方程可化为合流Heun类，并推导了相对论能量谱。
中文摘要 AI 辅助
我们研究了在外部磁场中(2+1)维Ellis可穿越虫洞上的带电Klein-Gordon模式，该磁场在辅助欧几里得嵌入空间中被定义为均匀的。空间几何本质上是悬链面形的，而嵌入仅用于构造外部规范连接。环境势的拉回产生了一个规则的方位角规范场，其相关的内在磁标量在喉部两侧改变符号。Klein-Gordon方程的分离导致了一个径向问题，该问题与具有规则有效势的一维薛定谔算子酉等价。对于非零磁耦合，二次渐近项在完整虫洞上产生径向约束。径向方程可以约化为合流Heun类。多项式截断仅在由同时终止条件确定的受限参数子流形上可能，因此并不代表一般的约束谱。我们推导了相应的相对论能量，并分析了最低多项式扇区，同时区分了形式上的连续ℓ可解性关联与标准角周期条件所需的方位角分离常数的整数值。
英文摘要
We study charged Klein-Gordon modes on a $(2+1)$-dimensional Ellis traversable wormhole in an external magnetic field defined as uniform in an auxiliary Euclidean embedding space. The spatial geometry is intrinsically catenoidal, while the embedding is used only to construct the external gauge connection. Pullback of the ambient potential yields a regular azimuthal gauge field whose associated intrinsic magnetic scalar reverses sign across the throat. Separation of the Klein-Gordon equation leads to a radial problem that is unitarily equivalent to a one-dimensional Schrödinger operator with a regular effective potential. For nonzero magnetic coupling, the quadratic asymptotic term produces radial confinement on the complete wormhole. The radial equation can be reduced to the confluent-Heun class. Polynomial truncation is possible only on constrained parameter submanifolds determined by simultaneous termination conditions and therefore does not represent the generic confined spectrum. We derive the corresponding relativistic energies and analyze the lowest polynomial sector, while distinguishing the formal continuous-$\ell$ solvability correlations from the integer values of the azimuthal separation constant required by the standard angular periodicity condition.
发表机构
- Erzurum Technical University（埃尔祖鲁姆技术大学）
- Eastern Mediterranean University（东地中海大学）
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