论文标题
引力辐射I的分解I：角度模式，完整性和引入伴随矛盾的谐波的双向谐波
Bi-orthogonal harmonics for the decomposition of gravitational radiation I: angular modes, completeness, and the introduction of adjoint-spheroidal harmonics
论文作者
论文摘要
辐射模式的估计是引力波理论中的一个核心问题，在信号建模和数据分析中具有重要的应用。大多数天体物理相关系统的模式在分析上可进行的模式使这个问题变得复杂。无处不在的解决方法是不使用模式，而是由旋转加权球形谐波定义的多极矩。但是，球形多极力矩仅与没有角动量的系统模式有关。结果，它们可以掩盖与天体物理相关系统的潜在物理，例如二进制黑洞合并和戒指。在这种情况下，时空动量意味着辐射模式不是球形的，而是球体本质上的。在这里，我们解决了与球体谐波有关的各种问题。我们首次表明，球体谐波不仅能够代表任意的引力波信号，而且还具有在一般相对论理论中未使用的一种正交性。 Along the way we present a new class of spin weighted harmonic functions dubbed ``adjoint-spheroidal" harmonics. These new functions may be used for the general estimation of spheroidal multipole moments via complete bi-orthogonal decomposition (in the angular domain). By construction, adjoint-spheroidal harmonics suppress mode-mixing effects known to plague spherical harmonic decomposition; as a result, they better approximate a系统的辐射模式，我们讨论了这些结果的潜在应用。
The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications in signal modeling and data analysis. This problem is complicated by most astrophysically relevant systems' not having modes that are analytically tractable. A ubiquitous workaround is to use not modes, but multipole moments defined by spin weighted spherical harmonics. However, spherical multipole moments are only related to the modes of systems without angular momentum. As a result, they can obscure the underlying physics of astrophysically relevant systems, such as binary black hole merger and ringdown. In such cases, spacetime angular momentum means that radiative modes are not spherical, but spheroidal in nature. Here, we work through various problems related to spheroidal harmonics. We show for the first time that spheroidal harmonics are not only capable of representing arbitrary gravitational wave signals, but that they also possess a kind of orthogonality not used before in general relativity theory. Along the way we present a new class of spin weighted harmonic functions dubbed ``adjoint-spheroidal" harmonics. These new functions may be used for the general estimation of spheroidal multipole moments via complete bi-orthogonal decomposition (in the angular domain). By construction, adjoint-spheroidal harmonics suppress mode-mixing effects known to plague spherical harmonic decomposition; as a result, they better approximate a system's true radiative modes. We discuss potential applications of these results. Lastly, we briefly comment on the challenges posed by the analogous problem with Teukolsky's radial functions
