AI 中文总结
该研究分析非对易背景下有效克尔类黑洞的视界、热力学及测地性质，推导热容量，发现变形使光子轨道内移、阴影缩小，修正类时圆轨道，得到不变光子频移。
AI 中文摘要
我们研究非对易背景下有效克尔类黑洞的视界结构、约束热力学及测地性质。变形通过依赖质量的类电荷贡献修改径向几何，同时保持测地方程的可分离性。我们确定视界存在的条件，识别极值零温构型，分析静止极限面与能层。特别关注模型的热力学解释，其中几何霍金量与固定非对易变形参数下约束态空间的共轭变量相区分。推导正则系综与巨正则系综的热容量，以表征其依赖系综的局域热行为。我们还得到球形光子区、赤道光环和阴影边界，表明变形使特征光子轨道向内移动并减小阴影整体尺寸。通过最内稳定圆轨道研究类时圆周运动，非对易修正使顺行与逆行分支均向内移动。最后，将发射器轨道方向与光子切向发射方向视为独立物理选择，得到不变光子频移。
英文摘要
We investigate the horizon structure, constrained thermodynamics, and geodesic properties of an effective Kerr-like black hole in a non-commutative background. Deformation modifies the radial geometry through a mass-dependent charge-like contribution, while preserving the separability of the geodesic equations. We determine the conditions for horizon existence, identify the extremal zero-temperature configuration, and analyze the stationary-limit surfaces and the ergoregion. Special attention is paid to the thermodynamic interpretation of the model, where the geometric Hawking quantities are distinguished from the conjugate variables associated with the constrained state space at fixed non-commutative deformation parameter. The canonical and grand-canonical heat capacities are derived to characterize their ensemble-dependent local thermal behavior. We also obtain the spherical photon region, equatorial light rings, and shadow boundary, showing that the deformation shifts the characteristic photon orbits inwards and reduces the overall size of the shadow. Timelike circular motion is studied through the innermost stable circular orbit, where non-commutative correction produces an inward shift of both the prograde and retrograde branches. Finally, invariant photon frequency shifts are obtained by treating the emitter's orbital direction and the photon's tangential emission direction as independent physical choices.
Comments21 pages, 5 figures
