  In this work we explore some mathematical physics aspects of the spherically
symmetric Lovelock black hole in high dimensions. Intended for this aim, we
thoroughly consider the metric corresponding to the five-dimensional Lovelock
black hole spacetime. We construct the strong retractions by the geodesic
equations on the background under consideration. As a result, from the
topological point of view, we construct the theory of strong homotopy retract,
which will allow us, in principle, to better understand some of its suitable
applications on astrophysics and cosmology, in particular, in the analysis of
the spacetime singularities. We find the solutions of the equation of motion
for both radial and angular coordinates, and then we describe the outer
("exterior") and lower ("interior") apparent horizons. Indeed, the outer
apparent horizon is the last surface from which the light waves could still
escape from the black hole. Thus, it is meaningful to analyze some physical
phenomena related to quantum particles propagating outside the exterior
apparent horizon, in particular, we discuss the quasistationary levels of
scalar fields and their radial wave functions, which are given in terms of the
general Heun functions. We also calculate the perihelion precession in this
background.
