In general relativity, an external observer cannot distinguish distinct internal structures between two spherically symmetric stars that have the same total mass M. However, when quantum corrections are taken into account, the external metrics of the stars will receive quantum corrections depending on their internal structures. In this paper, we obtain the quantum-corrected metrics at linear order in curvature for two spherically symmetric shells characterized by different internal structures: one with an empty interior and the other with N internal shells. The dependence on the internal structures in the corrected metrics tells us that geodesics on these backgrounds would be deformed according to the internal structures. We conduct numerical computations to find out the angle of geodesic precession and show that the presence of internal structures amplifies the precession angle reflecting the discrepancy between the radial and orbital periods within the geodesic orbit. The amount of the precession angle increases monotonically as the number of internal shells increases and it eventually converges to a certain value for N ⟶ ∞.

中文翻译：

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反映由壳组成的恒星内部结构的量子测地线


在广义相对论中，外部观察者无法区分总质量相同的两颗球对称恒星之间不同的内部结构中号。然而，当考虑到量子校正时，恒星的外部度量将根据其内部结构接受量子校正。在本文中，我们获得了两个具有不同内部结构的球对称壳的曲率线性阶量子校正度量：一个具有空的内部结构，另一个具有不同的内部结构。氮内壳。校正度量中对内部结构的依赖性告诉我们，这些背景上的测地线将根据内部结构而变形。我们进行数值计算来找出测地线进动的角度，并表明内部结构的存在放大了进动角，反映了测地线轨道内径向周期和轨道周期之间的差异。进动角的大小随着内壳数量的增加而单调增加，并最终收敛到某个值氮⟶ 无穷大。