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.

在这项工作中，我们探索了高维球对称洛夫洛克黑洞的一些数学物理方面。为了这个目的，我们彻底考虑了对应于五维拉夫洛克黑洞时空的度量。我们通过所考虑的背景上的测地线方程构建强收缩。因此，从拓扑的角度，我们构建了强同伦收缩理论，这将使我们从原则上更好地理解它在天体物理学和宇宙学中的一些合适的应用，特别是在时空分析中奇点。我们找到径向坐标和角坐标的运动方程的解，然后描述外部（“外部”）和下部（“内部”）视界。的确，外部视界是光波仍然可以从黑洞中逸出的最后一个表面。因此，分析一些与在外部视界外传播的量子粒子有关的物理现象是有意义的，特别是我们讨论了标量场的准平稳能级及其径向波函数，它们是根据一般 Heun 函数给出的。我们还在此背景下计算近日点岁差。