The radial Teukolsky equation for Kerr–Newman–de Sitter geometry: revisited

Dirac Equation on Kerr--Newman spacetime and Heun functions

“…The solutions to the radial Teukolsky equations (31), with two regular singularities at r = r ± and an irregular singularity at r = ∞, have been written in the form of series of hypergeometric functions [4]. Similar expressions as the ones in (32) have been found for the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric [40] and in the study of bosons in a Kerr-Sen black hole [41].…”

“…In order to study the radiation emitted by the black hole, one has to write down the wave function components near the exterior horizon, r → r + . Using (32), for z → 1, the (radial) components of Ψ defined in ( 12), ( 15) and ( 18) can be writte as…”

Wheeler equation in Kerr background and astrophysical jet collimation

“…3. It is interesting that, in 2021, Hortaçsu also encountered difficulty when he attempted to calculate the reflective coefficients at the event horizons in the Kerr background [21].…”

Radiation fluxes of gravitational, electromagnetic, and scalar perturbations in type-D black holes: an exact approach

“…Furthermore, these solutions have been utilized to calculate QNMs of the Teukolsky equation describing the Schwarzschild black hole [38], including its continuous spectrum [39], as well as for the central engine of Gamma-ray bursts (GRB) and cosmic jet of the Kerr black hole [40,41]. Following Fiziev's work, numerous researchers have employed Heun class functions to study source-free perturbation equations in various spacetimes, such as QNMs [42] of Dirac field in 2+1 dimensional GW background [43], QNMs and the reflection coefficient [44] of massless fields in Kerr-Newman-de Sitter BHs [45], and QNMs of the massive scalar field in Kerr-AdS 5 BHs [46]. Moreover, Cook et al [47] converted the modes equations of Kerr BHs into the confluent Heun equation and then solved the radial equation using the continued fraction method, and the angular equation using the spectral method, resulting in improved accuracy for the QNMs.…”