  We analyze the influence of the gravitational field produced by a slowly
rotating black hole with a cosmic string along the axis of symmetry on a
massive scalar field. Exact solutions of both angular and radial parts of the
Klein-Gordon equation in this spacetime are obtained, and are given in terms of
the confluent Heun functions. We emphasize the role of the presence of the
cosmic string in these solutions. We also investigate the solutions in regions
near and far from the event horizon. From the radial solution, we obtain the
exact wave solutions near the exterior horizon of the black hole, and discuss
the Hawking radiation of massive scalar particles.
