Spin weighted spheroidal harmonics
http://nielswarburton.net/BHPToolkit/Workshops/Warburton_BHPToolkit.pdf WebSpin-weighted spherical harmonics (SWSHs) generalize the standard spherical-harmonic functions. In particular, there is a spin weight s associated with each class of SWSHs s Y ℓ, m, and s = 0 corresponds to the standard spherical harmonics Y ℓ, m. They can be thought of as special cases of the Wigner D matrices.
Spin weighted spheroidal harmonics
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WebOct 21, 2024 · We do not find its particular advantage in this case because the angular Teukolsky equation ( 3) has a nice analogy with the scalar spheroidal harmonics or with the spin-weighted spherical harmonics. A merit is rather that one can easily test the isospectrality of these two eigenvalue problems.
WebOct 15, 2024 · There are a variety of alternative spherical harmonic systems. For example, spherical harmonic systems can be formulated in quaternion representation (see, e.g., K. Gürlebeck, W. Sprösig (2015)). Spherical harmonics may be generated in the framework of... WebApr 27, 2016 · Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on …
WebGeneralized (four-dimensional) spin-weighted spheroidal harmonics (SWSHs) were first defined by Teukolsky [11] in the context of black hole physics. They result from the … WebJulia package for evaluating and transforming Wigner's 𝔇 matrices, and spin-weighted spherical harmonics (which includes the ordinary scalar spherical harmonics). These functions are evaluated directly in terms of quaternions, as well as in the more standard forms of spherical coordinates and Euler angles. [1]
WebJun 20, 2024 · 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.
WebSpin-weighted spherical harmonics, sY, m, occur in many areas of physics—from quantum mechanics to geophysics. By contrast, spin-weighted spheroidal harmonics, Sγ s , m, are … chillige wallpapersWebSpinweighted spheroidal harmonics form a complete and orthonormal set of functions on a prolate spheroid. They are, however, not the eigenfunctions of the natural Laplace … chillige wallpaper pcWebMar 15, 2005 · Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and ... graceland sodexomywayWebMay 25, 2016 · The spin-weighted spherical harmonics may be constructed from the scalar spherical harmonics [64]; for s = 0, the spin-weighted and scalar spherical harmonics are related via the... graceland site crosswordWebJan 15, 2006 · Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and ... graceland sheds arkansasWebThe relationship between the spherical-harmonic tensors and spin-weighted spherical harmonics is derived. The results facilitate the spherical-harmonic expansion of a large class of tensor-valued ... graceland short filmWebpackage is just one way of computing spin-weighted spheroidal harmonics using the BHPToolkit You can also compute them in:-Sage using kerrgeodesic_gw (see Eric … graceland shoppe