  According to the no-hair theorem, astrophysical black holes are uniquely
characterized by their masses and spins and are described by the Kerr metric.
Several parametric deviations from the Kerr metric have been suggested to study
observational signatures in both the electromagnetic and gravitational-wave
spectra that differ from the expected Kerr signals. Due to the no-hair theorem,
however, such spacetimes cannot be regular everywhere outside the event
horizons, if they are solutions to the Einstein field equations; they are often
characterized by naked singularities or closed time-like loops in the regions
of the spacetime that are accessible to an external observer. For observational
tests of the no-hair theorem that involve phenomena in the vicinity of the
circular photon orbit or the innermost stable circular orbit around a black
hole, these pathologies limit the applicability of the metrics only to compact
objects that do not spin rapidly. In this paper, we construct a Kerr-like
metric which depends on a set of free parameters in addition to its mass and
spin and which is regular everywhere outside of the event horizon. We derive
expressions for the energy and angular momentum of a particle on a circular
equatorial orbit around the black hole and compute the locations of the
innermost stable circular orbit and the circular photon orbit. We demonstrate
that these orbits change significantly for even moderate deviations from the
Kerr metric. The properties of our metric make it an ideally suited spacetime
to carry out strong-field tests of the no-hair theorem in the electromagnetic
spectrum using the properties of accretion flows around astrophysical black
holes of arbitrary spin.
