Teukolsky-like equations with various spins 2024 in a deformed Kerr spacetime Hiroaki Nakajima1, Ya Guo2, and Wenbin Lin1, 2, ∗ Dec 1 School of Mathematics and Physics,23 University of South China, Hengyang, 421001, China 2 School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China[gr-qc] ∗Email: lwb@usc.edu.cn Abstract We study the wave equations with the various spins on the background of the Kerr metric deformed by a function of the radial coordinate, on which background we have studied the gravitational-wave equations previously.
We obtain the uni- fied expression of the Teukolsky-like master equations and the corresponding radial equations with various spins.
We find that taking the separable gauge introduced in previous study simplifies the unified form.
We also discuss the structure of thearXiv:2412.17878v1 radial equation as an ordinary differential equation, such as the existence of the reg- ular and the irregular singularities of the equation and the behavior of the solution around each singularity.
1 Introduction The study on the gravitational waves becomes much more important subject in cosmology than before, since the direct observation of gravitational waves by LIGO and Virgo [1].
The gravitational waves are described as a solution to the Einstein equation, where the metric is perturbed around a certain background.
As the source of the radiation of the gravitational waves, the dynamics of the binary system is often studied, since the analytical calculation is possible as well as the numerical simulation.
In particular, if the system is for the case of the extreme mass-ratio inspiral (EMRI), one can apply the black-hole perturbation theory [2], where the heavier object is regarded as the (black hole) background and the lighter one is regarded as a test particle.
if the mass ratio of the system is not so extreme, the background has to be deformed.
One systematic…