Rational orbits and gravitational waves in static spherical spacetimes: an open-source numerical framework -

[1]
LIGO Scientific and Virgo Collaboration, Phys. Rev. Lett.116, 061102 (2016), arXiv: 1602.03837
[2]
Event Horizon Telescope Collaboration, Astrophys. J. Lett.875, L1 (2019), arXiv: 1906.11238
[3]
Event Horizon Telescope Collaboration, Astrophys. J. Lett.930, L12 (2022)
[4]
M. Isi, W. M. Farr, M. Giesleret al., Phys. Rev. Lett.127, 011103 (2021), arXiv: 2012.04486
[5]
M. Takahashi and H. Koyama, Astrophys. J.693, 472 (2009), arXiv: 0807.0277
[6]
Z. Stuchlík and M. Kološ, Eur. Phys. J. C76, 32 (2016), arXiv: 1511.02936
[7]
R. Pánis, M. Kološ, and Z. Stuchlík, Eur. Phys. J. C79, 479 (2019), arXiv: 1905.01186
[8]
D. Li and X. Wu, Eur. Phys. J. Plus134, 96 (2019), arXiv: 1803.02119
[9]
S. Hu, X. Wu, and E. Liang, Astrophys. J. Suppl. S.257, 40 (2021), arXiv: 2108.09882
[10]
W. Sun, Y. Wang, F. Liuet al., Eur. Phys. J. C81, 785 (2021), arXiv: 2109.02295
[11]
Z. Huang, G. Huang, and A. Hu, Astrophys. J.925, 158 (2022)
[12]
L. Zhang, S. Chen, Q. Panet al., Eur. Phys. J. C83, 828 (2023), arXiv: 2309.12604
[13]
Z. Xu, D. Ma, W. Caoet al., Eur. Phys. J. C85, 770 (2025), arXiv: 2412.06122
[14]
O. Kopáček and V. Karas, Astrophys. J.787, 117 (2014), arXiv: 1404.5495
[15]
T. Jacobson and T. P. Sotiriou, Phys. Rev. Lett.104, 021101 (2010), arXiv: 0911.3363
[16]
S. W. Wei, Y. X. Liu, H. Guoet al., Phys. Rev. D82, 103005 (2010), arXiv: 1006.1056
[17]
M. Guo and S. Gao, Phys. Rev. D93, 084025 (2016), arXiv: 1602.08679
[18]
J. Levin and G. Perez-Giz, Phys. Rev. D77, 103005 (2008), arXiv: 0802.0459
[19]
M. Alloqulov, T. Xamidov, S. Shaymatovet al., Eur. Phys. J. C85, 798 (2025), arXiv: 2504.05236
[20]
V. Misra and J. Levin, Phys. Rev. D82, 083001 (2010), arXiv: 1007.2699
[21]
S. W. Wei, J. Yang, and Y. X. Liu, Phys. Rev. D99, 104016 (2019), arXiv: 1904.03129
[22]
C. Liu, C. Ding, and J. Jing, Commun. Theor. Phys.71, 1461 (2019), arXiv: 1804.05883
[23]
X. M. Deng, Phys. Dark Univ.30, 100629 (2020)
[24]
X. M. Deng, Eur. Phys. J. C80, 489 (2020)
[25]
H. Y. Lin and X. M. Deng, Phys. Dark Univ.31, 100745 (2021)
[26]
R. Wang, F. Gao,and H. Chen, Ann. Phys.447, 169167 (2022)
[27]
B. Gao and X. M. Deng, Ann. Phys.418, 168194 (2020)
[28]
H. Y. Lin and X. M. Deng, Eur. Phys. J. Plus137, 176 (2022)
[29]
J. Zhang and Y. Xie, Eur. Phys. J. C82, 854 (2022)
[30]
B. Gao and X. M. Deng, Mod. Phys. Lett. A36, 2150237 (2021)
[31]
H. Y. Lin and X. M. Deng, Universe8, 278 (2022)
[32]
H. Y. Lin and X. M. Deng, Eur. Phys. J. C83, 311 (2023)
[33]
Q. Qi, X. M. Kuang, Y. Z. Liet al., Eur. Phys. J. C84, 645 (2024), arXiv: 2407.01958
[34]
Y. K. Lim and Z. C. Yeo, Phys. Rev. D109, 024037 (2024), arXiv: 2401.13894
[35]
A. Bragado and G. J. Olmo, Class. Quant. Grav.42, 185004 (2025), arXiv: 2506.15600
[36]
S. Shaymatov, B. Ahmedov, M. De Laurentiset al., Astrophys. J.959, 6 (2023), arXiv: 2307.10804
[37]
T. Xamidov, S. Shaymatov, B. Ahmedovet al., JCAP01, 044 (2026), arXiv: 2503.06750
[38]
Z. Y. Tu, T. Zhu, and A. Wang, Phys. Rev. D108, 024035 (2023), arXiv: 2304.14160
[39]
L. Meng, Z. Xu, and M. Tang, Eur. Phys. J. C85, 306 (2025), arXiv: 2411.01858
[40]
Y. Z. Li, X. M. Kuang, and Y. Sang, Eur. Phys. J. C84, 529 (2024), arXiv: 2401.16071
[41]
C. H. Wang, X. C. Meng, Y. P. Zhanget al., JCAP07, 021 (2025), arXiv: 2502.08994
[42]
S. Lu, H. J. Lin, T. Zhuet al., Eur. Phys. J. C86, 283 (2026), arXiv: 2512.11911
[43]
S. Lu and T. Zhu, Phys. Dark Univ.50, 102141 (2025), arXiv: 2505.00294
[44]
T. Zahra, O. Shabbir, B. Majeedet al., Eur. Phys. J. C85, 1340 (2025), arXiv: 2510.22761
[45]
F. Ahmed, Q. Wu, S. G. Ghoshet al., JCAP02, 004 (2026), arXiv: 2511.08456
[46]
W. Deng, S. Long, Q. Tanet al., Chin. Phys. C50, 035103 (2026), arXiv: 2510.24468
[47]
M. Alloqulov, S. Shaymatov, B. Ahmedovet al., Eur. Phys. J. C86, 259 (2026), arXiv: 2511.15237
[48]
S. Yang, Y. P. Zhang, T. Zhuet al., JCAP01, 091 (2025), arXiv: 2407.00283
[49]
M. Alloqulov, S. Shaymatov, B. Ahmedovet al., Eur. Phys. J. C86, 117 (2026), arXiv: 2508.05245
[50]
L. Zhao, M. Tang, and Z. Xu, Eur. Phys. J. C85, 36 (2025), arXiv: 2411.01979
[51]
O. Shabbir, M. Jamil, and M. Azreg-Aïnou, Phys. Dark Univ.47, 101816 (2025), arXiv: 2501.04367
[52]
S. Haroon and T. Zhu, Phys. Rev. D112, 044046 (2025), arXiv: 2502.09171
[53]
C. Zhang and T. Zhu, Eur. Phys. J. C86, 350 (2026), arXiv: 2511.14080
[54]
E. L. B. Junior, J. T. S. S. Junior, F. S. N. Loboet al., Eur. Phys. J. C85, 557 (2025), arXiv: 2412.00769
[55]
S. Zare, T. Zhu, L. M. Nietoet al., JCAP01, 059 (2026), arXiv: 2510.05166
[56]
L. Huang, Phys. Rev. D111, 084038 (2025)
[57]
O. Shabbir, A. Shermatov, B. Majeedet al., Nucl. Phys. B1026, 117432 (2026), arXiv: 2601.02904
[58]
Z. Hua, Z. T. He, J. Q. Laiet al., Phys. Lett. B876, 140402 (2026), arXiv: 2601.00550
[59]
Y. Z. Li and X. M. Kuang, Eur. Phys. J. C86, 261 (2026), arXiv: 2509.07333
[60]
L. Huang and X. M. Deng, Phys. Rev. D109, 124005 (2024)
[61]
L. Huang, JCAP10, 067 (2025), arXiv: 2506.17909
[62]
H. Jiang, M. Alloqulov, Q. Wuet al., Phys. Dark Univ.46, 101627 (2024)
[63]
Y. H. Huang, S. Guo, Y. Lianget al., (2026), arXiv: 2606.16280
[64]
A. Kumar, A. Mohammadi, and S. G. Ghosh, (2026), arXiv: 2605.07187
[65]
T. Robson, N. J. Cornish, and C. Liu, Class. Quant. Grav.36, 105011 (2019), arXiv: 1803.01944
[66]
C. Caprini, A. Heffernan, R. Britoet al., (LISA Science), 2025, arXiv: 2507.05130
[67]
J. Luo, L. S. Chen, H. Z. Duanet al., Class. Quant. Grav.33, 035010 (2016), arXiv: 1512.02076
[68]
X. Y. Lu, Y. J. Tan, and C. G. Shao, Phys. Rev. D100, 044042 (2019), arXiv: 2007.03400
[69]
E. K. Liet al., Rept. Prog. Phys.88, 056901 (2025), arXiv: 2409.19665
[70]
W. H. Ruan, Z. K. Guo, R. G. Caiet al., Int. J. Mod. Phys. A35, 2050075 (2020), arXiv: 1807.09495
[71]
H. Liuet al., Research9, 1252 (2026)
[72]
S. Babak, H. Fang, J. R. Gairet al., Phys. Rev. D75, 024005 (2007), arXiv: gr-qc/0607007
[73]
L. S. Finn and K. S. Thorne, Phys. Rev. D62, 124021 (2000), arXiv: gr-qc/0007074
[74]
S. Tan, C. Jiang, D. Liet al., JHEP54, 100685 (2026), arXiv: 2604.13832