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The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ onKerr black hole spacetimes are investigated by solving the homogeneousTeukolsky equation numerically. The applied numerical setup is based on acombination of conformal compactification and the hyperbolic initial valueproblem. The evolved basic variables are expanded in terms of spin-weightedspherical harmonics which allows us to evaluate all the angular derivativesanalytically, whereas the evolution of the expansion coefficients, in thetime-radial section, is determined by applying the method of lines implementedin a fourth order accurate finite differencing stencil. Concerning theinitialization, in all of our investigations single mode excitations---eitherstatic or purely dynamical type initial data---are applied. Within this setupthe late time tail behavior is investigated. Due to the applied conformalcompactification the asymptotic decay rates are determined at threecharacteristic locations---in the domain of outer communication, at the eventhorizon and at future null infinity---simultaneously. Recently introduced newtype of `energy' and `angular momentum' balance relations are also applied inorder to demonstrate the feasibility and robustness of the developed numericalschema, and also to verify the proper implementation of the underlyingmathematical model.

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