Geometric transformations on a topological black hole and their applications

Abstract

Abstract Topology and geometry can be used to classify interpretation of many astronomical phenomena in our universe. We characterize the spherical topology of black holes in a special case of spherical symmetry. For this purpose, we carefully consider the metrics space of topological black holes B 4 . By adjusting some of the parameters, we infer the appropriate components and the equatorial geodesics on the line element of the topological black holes. We also construct the minimal retraction ρ 2 : B 4 → C 2 3 . As a result, the minimal deformation retract has also been inferred to explain the effects on their center of mass in binary system. This would help us to better understand some of possible applications in astrophysics and cosmology, such as the natural phenomenon of a distinctive gravitational wave signature of merging two black holes associated with curved space–time in general relativity. In addition, we discuss the relation between limit folding and limit minimal retraction on the n -dimension. Under the folding map on the connected sum of essential sub-manifolds, the topological black hole can be constructed for different types and characteristics.