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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃宇廷 | zh_TW |
| dc.contributor.advisor | Yu-tin Huang | en |
| dc.contributor.author | 謝天 | zh_TW |
| dc.contributor.author | Tien Hsieh | en |
| dc.date.accessioned | 2023-08-16T16:40:15Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-08-16 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-08 | - |
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Casals, “Eigenvalues and eigenfunctions of spin weighted spheroidal harmonics in four and higher dimensions,” Phys. Rev. D, vol. 73, p. 024013, 2006. [Erratum: Phys.Rev.D 73, 109902 (2006)]. [24] D. R. Brill, P. L. Chrzanowski, C. M. Pereira, E. D. Fackerell, and J. R. Ipser, “Solution of the Scalar Wave Equation in a Kerr Background by Separation of Variables,” Physical review, vol. 5, pp. 1913–1915, 4 1972. [25] J. N. Goldberg, A. Macfarlane, E. T. Newman, F. Rohrlich, and E. C. G. Sudar shan, “Spin-s Spherical Harmonics and ð,” Journal of Mathematical Physics, vol. 8, pp. 2155–2161, 1 1967. [26] E. W. Leaver, “An Analytic representation for the quasi normal modes of Kerr black holes,” Proc. Roy. Soc. Lond. A, vol. 402, pp. 285–298, 1985. [27] Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, “Scattering in black hole backgrounds and higher-spin amplitudes. Part I,” JHEP, vol. 03, p. 136, 2023. [28] Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines, “Scattering in Black Hole Backgrounds and Higher-Spin Amplitudes: Part II,” 12 2022. [29] N. Arkani-Hamed, T.-C. Huang, and Y.-t. Huang, “Scattering amplitudes for all masses and spins,” JHEP, vol. 11, p. 070, 2021. [30] H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Grav ity. Cambridge University Press, 2 2015. [31] N. Arkani-Hamed, Y.-t. Huang, and D. O’Connell, “Kerr black holes as ele mentary particles,” JHEP, vol. 01, p. 046, 2020. [32] R. Aoude and A. Ochirov, “Classical observables from coherent-spin ampli tudes,” JHEP, vol. 10, p. 008, 2021. [33] M. Richartz, “Quasinormal modes of extremal black holes,” Physical review, vol. 93, 3 2016. [34] A. M. Perelomov, “Generalized Coherent States and Some of their Applications. 1.,” Usp. Fiz. Nauk, vol. 123, pp. 23–55, 1977. [35] M.-Z. Chung, Y.-T. Huang, and J.-W. Kim, “Classical potential for general spinning bodies,” Journal of High Energy Physics, vol. 2020, 9 2020. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/88990 | - |
| dc.description.abstract | 黑洞的準正規模式來自於黑洞微擾理論的角度方向和徑向的解。這些模式代表了重力波在黑洞背景下傳遞的獨特頻率和衰減速率，例如雙黑洞系統中的重力波發射。
本論文探討了在使用自旋-螺旋形式時，利用涉及重力子發射的在殼三點樹級散射振幅，來描述黑洞準正規模式的角度向特殊函數。受到主導黑洞準正規模式的微擾度量的洛倫茲不變性的啟發，我們利用自旋-螺旋形式來表示史瓦西黑洞準正規模式的角度向特殊函數，即自旋加權球諧函數，並以不同自旋配置的不等質量振幅來表示。 接著，通過結合可用於描述古典自旋的自旋相干態和來自不等質量散射過程的在殼方法，這個被建構的張量，即具有自旋配置的在殼相干張量，可以重現克爾黑洞準正規模式的角度向特殊函數，即自旋加權橢球諧函數。 總體而言，本研究提供了一個框架，利用具有SU(2)自旋配置的在殼自旋-螺旋形式，來理解SO(3)表示的球對稱和旋轉黑洞準正規模式的角度向特殊函數。 | zh_TW |
| dc.description.abstract | Quasinormal Modes (QNMs) of black holes are from the angular and radial so lution of the Black Hole Perturbation Theory (BHPT). These modes represent the unique transmitted frequencies and decay rates of the gravitational waves under a background of the black hole metric, such as the emission of gravitational waves in binary black hole system.
This thesis explores the application of the spinor-helicity formalism in using on shell 3pt tree-level scattering amplitudes involving graviton emissions to describe the angular dependence of the black hole QNMs. The Lorentz invariance of the perturbed metrics, which govern the black hole QNMs, motivate us to represent the angular dependence of the Schwarzschild QNMs, the spin-weighted spherical harmonics, by the unequal masses amplitudes using the spinor-helicity formalism with different spin configurations. Then, by combining the coherent spin state which can be used to describe a classical spin and the on-shell elements from unequal masses scattering process, the constructed tensors, which are called the on-shell coherent tensors with spin configurations, can reproduce the angular dependence of the of Kerr QNMs, the spin-weighted spheroidal harmonics. Overall, this research provides a framework for understanding the angular de pendence of spherically symmetric and rotating black hole QNMs which are SO(3) representation by using the on-shell spinor-helicity formalism with the SU(2) spin configurations. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-16T16:40:15Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-08-16T16:40:15Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 謝辭 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 Introduction 1 2 Background on Black Hole Perturbation Theory 9 2.1 Regge-Wheeler–Zerilli equation for Schwarzschild Black Hole QNMs . 10 2.2 Teukolsky equation for Kerr Black Hole QNMs . . . . . . . . . . . . . 12 3 Spin-weighted Spherical Harmonics from On-shell Kinematics (Schwarzschild) 24 3.1 Spinor-Helicity Formalism and Unequal Mass 3pt Amplitude . . . . . 25 3.2 Setup of On-shell Spinors . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Spin-weighted Spherical Harmonics . . . . . . . . . . . . . . . . . . . 33 4 Spin-weighted Spheroidal Harmonics from On-shell Kinematics (Kerr) 36 4.1 Review of Coherent Spin State . . . . . . . . . . . . . . . . . . . . . . 37 4.2 Spin-weighted Spheroidal Harmonics . . . . . . . . . . . . . . . . . . 45 5 Discussion and Conclusion 55 A Review of Coherent State 58 B Example of Coherent Tensors 62 Bibliography 67 | - |
| dc.language.iso | en | - |
| dc.subject | 散射振幅 | zh_TW |
| dc.subject | 準正規模式 | zh_TW |
| dc.subject | 黑洞微擾理論 | zh_TW |
| dc.subject | 克爾黑洞 | zh_TW |
| dc.subject | 史瓦西黑洞 | zh_TW |
| dc.subject | 在殼方法 | zh_TW |
| dc.subject | 自旋螺旋形式 | zh_TW |
| dc.subject | Spinor-helicity formalism | en |
| dc.subject | Scattering amplitude | en |
| dc.subject | Quasinormal modes | en |
| dc.subject | Black hole perturbation theory | en |
| dc.subject | Schwarzschild black holes | en |
| dc.subject | Kerr black holes | en |
| dc.subject | On-shell methods | en |
| dc.title | 在殼方法應用於黑洞準正規模式之散射振幅研究 | zh_TW |
| dc.title | On-shell Amplitude of Black Hole Quasinormal Modes | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳恒榆;賀培銘;太田信義 | zh_TW |
| dc.contributor.oralexamcommittee | Heng-Yu Chen;Pei-Ming Ho;Nobuyoshi Ohta | en |
| dc.subject.keyword | 散射振幅,自旋螺旋形式,在殼方法,史瓦西黑洞,克爾黑洞,黑洞微擾理論,準正規模式, | zh_TW |
| dc.subject.keyword | Scattering amplitude,Spinor-helicity formalism,On-shell methods,Schwarzschild black holes,Kerr black holes,Black hole perturbation theory,Quasinormal modes, | en |
| dc.relation.page | 71 | - |
| dc.identifier.doi | 10.6342/NTU202302187 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-08-09 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| 顯示於系所單位： | 物理學系 | |
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