COSAM » Events » 2016 » April » Algebra/Linear Algebra Seminar

 Algebra/Linear Algebra Seminar Time: Apr 12, 2016 (04:00 PM) Location: Parker Hall 224 Details: Speaker: Professor Guihua Tian, Department of Physics, Beijing University of Posts and Telecommunications Title: Research on the recurrence relations for the spin-weighted spheroidal harmonics Abstract: The spin-weighted spheroidal harmonics (SWSHs) are first defined by Teukolsky in the study of the perturbation of the Kerr black holes. They are the extension of the spin-weighted spherical harmonics and important for the study of the perturbation of the Kerr blackhole. The spin-weight $$s$$ of SWSHs can be $$0, \pm 1/2, \pm 1, \pm 3/2, \pm 2$$, and the corresponding perturbation fields to Kerr blackhole are the scalar, neutrino, electromagnetic, Rarita-schwinger, and gravitational ones, respectively. The spheroidal harmonics are SWSHs when the spin-weight is zero. The spheroidal harmonics are easier to study than the counterparts of the spin-weight $$s \neq 0$$. Through the methods in super-symmetric quantum mechanics, we study the recurrence relations for SWSHs with different spin weight. These relations can be applied to derive SWSHs of $$s = \pm 1, \pm 2$$ from the spheroidal functions, that is SWSHs of $$s = 0$$. They also give SWSHs of $$s = -1/2, \pm3/2$$ from that of $$s = 1/2$$. These recurrence relations are first investigated and are very important both in theoretical background and the astrophysical applications. Keywords: spin-weighted spheroidal harmonics, recurrence relation, super-symmetric quantum mechanics, shape-invariance PACS numbers: 02.30.Gp, 03.65.Ge, 11.30.Pb

Last updated: 04/11/2016