博纳诺 - 罗伊特正则黑洞周围的周期轨道和引力波特征

中文摘要 AI 辅助

在博纳诺 - 罗伊特正则黑洞时空研究类时测地线、周期轨道及其相关引力波特征。该黑洞源于渐近安全引力，用德西特核心取代中心奇点。无量纲参数α/M²决定强场动力学。通过有理频率比q分类轨迹发现周期轨道有向内收缩。在数值框架下计算极端质量比吸积的引力波极化，渐近安全修正导致相位左移、峰值幅度略有增强。波形敏感性强烈依赖拓扑，未来天基探测器可探测到这种内在量子引力修正产生的独特特征。

英文摘要

Timelike geodesics, periodic orbits, and their associated gravitational-wave signatures are examined in the spacetime of a Bonanno--Reuter regular black hole, a geometry arising from Asymptotically Safe Gravity in which a running Newton coupling replaces the central singularity with a de Sitter core. The dimensionless parameter $α/M^2$ completely determines the strong-field dynamics. Increasing $α/M^2$ shifts the marginally bound and innermost stable circular orbits inward, systematically reducing their characteristic radii, angular momenta, and energies; the allowed phase space for bound motion contracts accordingly. Classifying trajectories via the rational frequency ratio $q = w + v/z$ reveals that periodic orbits experience a mild inward contraction, which reduces the energy necessary to sustain a specific topology. Within the numerical kludge framework, we calculate the gravitational-wave polarizations for extreme mass-ratio inspirals. The asymptotically safe correction induces a leftward phase shift that reflects shorter orbital periods, while mildly enhancing peak amplitudes owing to the smaller periastron distances reached in the deep strong-field regime. Waveform sensitivity displays a strong dependence on topology, with high-whirl orbits, which persist longer in the strong-field region near the horizon, showing markedly more pronounced deviations. Unlike environmental effects that inflate orbital scales, intrinsic quantum-gravity modifications generate distinct, observationally detectable signatures for future space-based detectors such as LISA, Taiji, and TianQin.

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13 pages, 7 figures,