发表机构
SISSA; INFN Sezione di Trieste; IFPU – Institute for Fundamental Physics of the Universe（的里雅斯特国际高等研究学院; 意大利国家核物理研究所的里雅斯特分部; 宇宙基础物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对黑洞光环上的光子，通过相关方程解析推导其引力辐射的多极功率规律，发现总功率对数发散，还修正了前人关于有质量粒子同步辐射的结果，且与数值解验证一致。
AI 中文摘要
施瓦西或克尔黑洞圆类光测地线上的无质量粒子会辐射出所有多极阶的引力波$\ell$，其功率仅以$1/\ell$的形式衰减，导致总瞬时功率呈对数发散。我们以零应力能量张量为源，通过Zerilli–Regge–Wheeler方程和Teukolsky方程解析推导了该结果，发现辐射到无穷远的功率与被视界吸收的功率均趋近于$\dot{E}_\ell\to g(a) \kappa E^2/(M^2\ell)$，其中$E$为粒子能量，$M$为黑洞质量，$a$为其自旋，$\kappa=0.063653$为某参数，$g(a)$为自旋因子，我们针对任意自旋，以克尔光环半径$r_0$得到了其闭式表达式$g=27M^2(r_0-M)/[r_0^2(r_0+3M)]$。$1/\ell$行为有两个成因：一是光子与准正则模式的近共振，其阻止了大$\ell$处的任何指数抑制；二是无质量粒子特有的源抵消，其使每极功率相对于一般源降低了因子$\ell^2$。在领头阶，一半辐射落入黑洞，我们计算了无自旋情况下该等分的一阶修正。相同分析适用于靠近光环轨道的有质量粒子，其中质量将$1/\ell$定律转变为指数截断。我们得到了Breuer、Ruffini、Tiomno和Vishveshwara（1973）提出的有质量粒子测地线同步辐射公式的主导偶宇称项，但发现他们的奇宇称项小了4倍。所有结果均与数值解对比验证，施瓦西情况最高到$\ell=12800$，克尔情况最高到$\ell=800$。
英文摘要
A massless particle on the circular null geodesic of a Schwarzschild or Kerr black hole radiates gravitational waves at all multipoles $\ell$ with a power that falls off only as $1/\ell$, so that the total instantaneous power is logarithmically divergent. We derive this result analytically from the Zerilli--Regge--Wheeler and Teukolsky equations with a null stress-energy tensor as source, and find that both the power radiated to infinity and the power absorbed by the horizon approach $\dot{E}_\ell\to g(a) κE^2/(M^2\ell)$, where $E$ is the energy of the particle, $M$ the mass of the black hole and $a$ its spin, with $κ=0.063653$ and a spin factor $g(a)$, for which we obtain, for any spin, the closed form $g=27M^2(r_0-M)/[r_0^2(r_0+3M)]$ in terms of the radius $r_0$ of the Kerr light ring. The $1/\ell$ behavior has two causes: the near-resonance of the photon with the quasinormal modes, which prevents any exponential suppression at large $\ell$, and a cancellation in the source that is specific to massless particles, which reduces the power per multipole by a factor $\ell^2$ with respect to a generic source. At leading order half of the radiation falls into the black hole, and we compute the first correction to this equal split in the non-spinning case. The same analysis describes massive particles on orbits close to the light ring, where the mass turns the $1/\ell$ law into an exponential cut-off. We recover the dominant, even-parity term of the geodesic synchrotron radiation formulae for massive particles of Breuer, Ruffini, Tiomno and Vishveshwara (1973), but we find that their odd-parity term is too small by a factor of four. All results are checked against numerical solutions, up to $\ell=12800$ in Schwarzschild and $\ell=800$ in Kerr.
Comments12 pages, 2 figures. Companion repository at github.com/enricobarausse/photon-lightring-fluxes
