Abstract <p>The problem of finding solutions to the Klein–Gordon equation for a real scalar field in the spacetime of an axially symmetric black hole described by the Kerr metric is considered. It is shown that the radial and angular parts of this equation can be reduced to the form of a confluent Heun equation. Physically adequate solutions to the radial equation, expressed through confluent Heun functions, are found and their normalizations are calculated. Compared to the case of Minkowski space, a doubling of the number of physically adequate solutions with energy greater than that of the particle mass has been observed.</p>