Some aspects of the five-dimensional Lovelock black hole spacetime: strong homotopy retract, perihelion precession and quasistationary levels

TL;DR

This paper investigates the mathematical and physical properties of five-dimensional Lovelock black holes, including topology, horizons, quantum scalar fields, and perihelion precession, providing new insights into high-dimensional black hole physics.

Contribution

It introduces the theory of strong homotopy retracts for Lovelock black holes and analyzes physical phenomena like horizons, scalar field levels, and perihelion precession in this context.

Findings

Constructed strong retractions via geodesic equations.

Derived solutions for scalar fields using Heun functions.

Calculated perihelion precession in five-dimensional Lovelock spacetime.

Abstract

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.