Exploring Absolute Retract in Regular Hayward Black Holes and Their Implications for Astrophysics

In this article, we study and describe the topology of the spherically symmetric and regular (with no singularity in its event horizon) black hole, which is called Hayward black hole. We use the symmetric metric for this object, associated with the Euler-Lagrangian equation, to derive various types of geodesic equations and components of a subspace geodesic. Under certain conditions, this approach allows us to deduce three types of absolute retractions representing the particle's motion along different axes within a 3-D subspace. These retractions could potentially describe the region of the event horizon of Hayward black holes. We show that the radial geodesics describe motion directly toward the black hole's center, while tangential geodesics illustrate paths without angular displacement. Spacetime curvature near the event horizon emphasizes the intense gravitational effects and distortions caused by the black hole's mass. Particle motion in subspace ${\mathscr{H}}_3$ represents constrained tangential dynamics, providing insights into localized spacetime. In addition, the study of the Hayward black hole (topology and geometry) is valuable for our understanding of general relativity, exploring the quantum field of gravity implications, and contribute to the fields of mathematical physics and astrophysics.