Abstract
A good way to explore the characteristics of a black hole is to consider the influence of perturbation due to background spacetime. The key to perturbation is to solve the wave function of the test particles. The main purpose of this paper is to study the perturbations of the Grumiller black hole. The Grumiller metric includes a Rindler term, which leads to an anomalous acceleration in geodesics of test particles. We investigate the perturbation equations of the massless scalar,neutrino, electromagnetic, Rarita-Schwinger and gravitational fields propagating on this background by using NewmanPenrose formalism. We obtain the Teukolsky-type master equation governing these fields. The master equation can be separated into its angular and radial parts. The former is the equation of a spin-weighted spherical harmonic, and the latter is an Heun's equation in disguise, for which we are able to use a known technique to analyze solutions. As examples, the radial wave function near the event horizon is given. All these results are the foundation for the study of perturbation effect of the Grumiller black hole.
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