A spherically topological analysis of stationary black holes

A black hole with zero angular momentum is said to be stationary and under certain conditions such a black hole can represented as a sphere. This review examines Hawking’s topology theorem, the Schwarzschild metric, novel solutions to Einstein’s equations, resonances of hyperbolic orbits around the event horizon for spherical, stationary black holes, and analyzes their importance. It is suggested, that in the spherical stationary black hole case, the Fourier analysis can be used to find the resonances due to Geometric scattering of hyperbolic orbits and thus the outgoing energy fields from the event horizon can be found more precisely; allowing for the adequate signal processing analysis to be found for such a field.