We investigate analytically the power radiated by a scalar particle in circular geodesic orbits around a Schwarzschild black hole. The radial scalar field modes are written in terms of confluent Heun functions. We obtain the emitted power using the framework of Quantum Field Theory in Curved Spacetimes at tree level. We compare our analytical results with the numerical ones, obtaining excellent agreement. The use of confluent Heun functions to describe the radial modes may also be extended to fields of different spins in other black hole spacetimes.

中文翻译：

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黑洞时空的测地线同步辐射：分析研究

我们分析了一个标量粒子在围绕 Schwarzschild 黑洞的圆形测地轨道中辐射的功率。径向标量场模式用汇合 Heun 函数表示。我们在树级别使用弯曲时空中的量子场论框架获得发射功率。我们将我们的分析结果与数值结果进行比较，获得了极好的一致性。使用汇合 Heun 函数来描述径向模式也可以扩展到其他黑洞时空的不同自旋场。