We computed the orbital evolution and the emitted gravitational radiation of the supermassive black hole binary OJ 287. Here we used the initial data provided by the outburst structure of the system. We considered the spin–spin, spin–orbit, and the next-to-next leading order fourth post-Newtonian (4PN) corrections in our analysis. In this way, we could make an accurate examination of unstable orbits (3M < r < 6M) of the secondary black hole. We tested the 4PN terms by analyzing the total and radiated energy, compared the post-Newtonian parameters and the separation of the two black holes for 3PN and 4PN. In conclusion, the 4PN corrections provided a significantly more accurate tool for analyzing unstable orbits than earlier 3PN terms. Furthermore, in this paper, we show the strain of gravitational waves emitted by OJ 287 during its complete orbital evolution including unstable orbits.

中文翻译：

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OJ 287后牛顿四阶轨道演化与引力波

我们计算了超大质量黑洞双星 OJ 287 的轨道演化和发射的引力辐射。这里我们使用了系统爆发结构提供的初始数据。在我们的分析中，我们考虑了自旋-自旋、自旋-轨道和紧随其后的第四次后牛顿 (4PN) 校正。这样，我们就可以对不稳定轨道（3米<r< 6米) 的次级黑洞。我们通过分析总能量和辐射能量来测试 4PN 项，比较后牛顿参数和 3PN 和 4PN 两个黑洞的分离。总之，4PN 校正为分析不稳定轨道提供了比早期 3PN 项更准确的工具。此外，在本文中，我们展示了 OJ 287 在其包括不稳定轨道在内的完整轨道演化过程中发射的引力波应变。