The quasinormal modes of non-rotating black holes and wormholes

At the beginning of the last century, solutions to the Einstein equation indicated the existence of mysterious objects, later called black holes. The Schwarzschild metric describes the geometry of the space-time of a black hole with the presence of two singularities. One of them is called the event horizon, in the vicinity of which gravity is extreme, which leaves the question of the truth of the Schwarzschild geometry open. Direct and indirect observations, such as the study of quasi-normal modes, are likely to be the most valuable for studying the structure of a black hole. Quasi-normal modes are the response to the perturbation of the geometry of a black hole. The mathematical structure of such modes is quite nontrivial, and these are complex functions oscillating at a "frequency" that is a complex number. The real part is the oscillation frequency while the imaginary gives the rate at which oscillations are damped. A more mysterious object that may exist in the universe is a wormhole, geometrically outwardly imitating a black hole. This fact may cause some inaccuracy when observing an astrophysical object. Comparing the perturbation profiles of these objects allows us to see that the quasi-normal modes of a black hole obey the characteristic ringdown signal. At the same time, for a wormhole, it theoretically turns out that the quasi-normal modes are a series of echoes representing a periodically repeating signal.