  In a talk given in 2013, S. Hawking conjectured that the event horizon of
black holes does not exist and suggested redefining black holes as bound states
of the gravitational field. Inspired by this idea, we investigated the coupling
of the Bardeen action and a complex scalar field model. Numerically, we
obtained a class of boson stars solutions with the magnetic monopole charge
$q$. When the constant $q$ exceeds a certain threshold, we observed that as the
frequency approaches zero, a critical position $r_c$ emerges where the scalar
field concentrates within its interior. Outside this critical position, these
boson star solutions tend to infinitely approach what is known as an extreme
black hole. However, there is no event horizon present. While our results are
model-dependent and their generality remains uncertain, they align well with
Hawking's conjecture that real, regular black holes do not have an event
horizon and provided valuable insights into the understanding and development
of concepts such as fuzzballs, firewalls and black hole soft hairs.
