# Numerical investigation of the dynamics of linear spin $s$ fields on Kerr background I. Late time tails of spin $s = \pm 1, \pm 2$ fields

## TL;DR

This paper numerically studies the late-time decay of linear spin $s=\pm 1,\, \pm 2$ fields on Kerr black holes, analyzing their behavior at different characteristic locations using conformal compactification and advanced numerical methods.

## Contribution

It introduces a robust numerical framework combining conformal compactification and spectral methods to analyze spin fields on Kerr backgrounds, including new decay rate measurements at multiple locations.

## Key findings

- Determined decay rates of spin fields at horizon, infinity, and in the domain of outer communication.
- Validated the numerical approach using energy and angular momentum balance relations.
- Confirmed the robustness and accuracy of the method for late-time tail analysis.

## Abstract

The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics which allows us to evaluate all the angular derivatives analytically, whereas the evolution of the expansion coefficients, in the time-radial section, is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations single mode excitations---either static or purely dynamical type initial data---are applied. Within this setup the late time tail behavior is investigated. Due to the applied conformal compactification the asymptotic decay rates are determined at three characteristic locations---in the domain of outer communication, at the event horizon and at future null infinity---simultaneously. Recently introduced new type of `energy' and `angular momentum' balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema, and also to verify the proper implementation of the underlying mathematical model.