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

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.