Recent gravitational wave detections from black hole mergers have underscored the critical role black hole perturbation theory and the Teukolsky equation play in understanding the behaviour of black holes. The separable nature of the Teukolsky equation has long been leveraged to study the vacuum linear Teukolsky equation; however, as theory and measurements advance, solving the sourced Teukolsky equation is becoming a frontier of research. In particular, second-order calculations, such as in quasi-normal mode and self-force problems, have extended sources. This paper presents a novel method for analytically separating the Teukolsky equation's source, aimed to improve efficiency. Separating the source is a non-trivial problem due to the angular and radial mixing of generic quantities in Kerr spacetime. We provide a proof-of-concept demonstration of our method and show that it is accurate, separating the Teukolsky source produced by the stress-energy tensor of an ideal gas cloud surrounding a Kerr black hole. The detailed application of our method is provided in an accompanying \textit{Mathematica} notebook. Our approach opens up a new avenue for accurate black hole perturbation theory calculations with sources in both the time and frequency domain.
Solutions to the Angular Teukolsky Equation have been used to solve various applied problems in physics and are extremely important to black-hole physics, particularly in computing quasinormal modes and in the extreme-mass-ratio inspiral problem. The eigenfunctions of this equation, known as spin-weighted spheroidal functions, are essentially generalizations of both the spin-weighted spherical harmonics and the scalar spheroidal harmonics. While the latter functions are quite well understood analytically, the spin-weighted spheroidal harmonics are only known analytically in the spherical and o…
High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such a way that the problem can be reformulated as a wave equation in an auxiliary spacetime in which the proof of stability is greatly simplified, owing to the absence of an ergoregion. As a preliminary step towards extending these ideas to higher-dimensional black holes, we study the mode stability of the massless scalar wave equation in the five-dimensional b…
Analytical derivation of long-term dephasing caused by phase transitions in the context of Kerr black holes
Faculty of Physics, Lomonosov Moscow State University（莫斯科国立大学物理系）；International School, I.M. Sechenov First Moscow State Medical University（伊万·谢切诺夫第一莫斯科国立医科大学国际学院）
We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an osc…
Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existe…
Quasinormal modes of Kerr-Newman-de Sitter black holes from Heun connection formulae
Toyota Technological Institute（丰田技术研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；Tokyo Metropolitan University（东京都立大学）；Nagoya University（名古屋大学）
\begin{abstract} Using the Keeton and Petters approach, we determine the deflection angle. We also investigate the motion of photons around a parameterized black hole in the presence of non-magnetized cold plasma by using a new ray-tracing algorithm. In spherically symmetric spacetime, we examine the influence of the plasma by applying the Hamiltonian equation on the deflection angle as well as shadow. It is examine to derive the rays analytically from Hamilton's equation by separating the metric and the plasma frequency. We study that the presence of plasma affects the deflection angle as wel…
