  Usually alternative theories of gravity imply deviations from the well-known
Kerr space-time, a model of an isolated black hole in General Relativity. In
the dominant order, the deformed Kerr metric, free of closed time-like curves
outside the event horizon, has been suggested recently by Johannsen and
Psaltis. It has a single deformation parameter which is not constrained by the
current observations, allowing, thereby, for a kind of unified and simple
phenomenological description of black holes in various theories of gravity.
Here we consider a number of classical and quantum phenomena of radiation in
the vicinity of such deformed Schwarzschild-like and Kerr-like black holes:
spiralling of particles into black holes, decay of fields propagating in the
black hole's background, Hawking radiation. In particular, we calculate some
quantitative characteristics of the above phenomena, such as the binding energy
of particles, quasinormal modes, late-time tails of fields of various spin,
intensity of Hawking radiation. The binding energy released when a particle
goes over from a given stable orbit in the equatorial plane to the innermost
stable one is calculated for such non-Kerr black holes. Due to inseparability
of the wave equations in the general case, the perturbations and stability of
scalar, Dirac, and electromagnetic fields are analyzed for vanishing rotation
only. The dependence of the radiation phenomena on the deformation parameter is
discussed.
