  In absence of explicit solutions of the perturbation equation of a static
symmetrical homogeneous space-time, the best we can do is to construct a {\it
quasi-}transformation. In this framework, we solve the perturbation equation
with initial data and a number of results are derived. Far from the horizon of
a black hole of even space dimension $N$, a mass-less field decays as ${r^l}
{{(-{r^2}+{t^2})}^{\frac{1-N}{2}-l}}$ in space-time, where $l$ is a harmonic
number of the sphere. A relation of energy and momentum of a particle with mass
in a hyper black hole is discovered and a solution to the equation of
Klein-Gordon in the metric of Schwarzschild-Tangherlini with initial data on
the hypersphere is proposed. Also, the Green's function of the Klein-Gordon
equation in Schwarzschild coordinates is calculated. This function is a sum on
the harmonic modes of the sphere. The first term is a double integration on the
spectrum of energy and the momentum of the particle. Far from the horizon, the
double integration is approximated by an integration on a line defined by the
relation of energy and momentum of a free particle. From here, the potential of
Yukawa is derived. Finally, the linear perturbation equations are derived and
solved exactly.
