  Black hole (BH) solution in the conformal Weyl gravity is a generalization of
the Schwarzschild spacetime which includes two additional constants appearing
when integrating the third order differential equations for gravitational
field. One constant looks like the effective cosmological constant providing
the de Sitter asymptotic of the solution. The other constant allows one to
describe flat rotation of galaxies without introducing of the dark matter. Here
we show that the effective "dark matter" term in the metric function
drastically changes the asymptotic behavior of the evolution of the wave
function of a scalar field: after the Schwarzschild-like ringing phase, the
ringing at another, non-Schwarzschildian, longer-lived frequency takes place
before the beginning of the exponential asymptotic tail. Thus the evolution of
the scalar field consists of the three qualitatively different stages: the
Schwarzschild-like ringing phase, the effective dark matter ringing phase and
the de Sitter phase characterized by exponential tails. The late time behavior
of the electromagnetic field is qualitatively different as well: the
exponential tails appear even in the absence of the effective de Sitter term.
