Quasinormal modes correspondence between horizonless asymptotically regular flat spacetimes and asymptotically anti–de Sitter black holes

This article investigates the quasinormal modes (QNMs) features of regular asymptotically flat spacetimes using Hayward and Bardeen spacetimes as examples. It is found that, using tortoise coordinates ${r}_{*}$, the boundary conditions for QNMs in horizonless asymptotically flat regular (HFR) spacetime are similar to those of asymptotically anti--de Sitter (AAdS) black holes. Subsequently, this work demonstrates quasinormal mode oscillations in both types of spacetime using finite difference methods and observe certain similarities in their QNM characteristics. What is more, our results by the matrix method also show the proportional relationships: $\ensuremath{\omega}\ensuremath{\propto}{r}_{p}$ for large event horizon ${r}_{p}$ in extremal AAdS black hole spacetime and $w\ensuremath{\propto}\sqrt{{f}_{o}}$ for large values of extremum of shift function ${f}_{o}$ in HFR spacetime. These similar characteristics suggests that studying the properties of extremal AAdS black holes could provide insights into HFR spacetime, as well as similar spacetimes like gravastars or compact objects. Additionally, this work also show that the potential function for QNMs in HFR spacetime with small ${f}_{o}$ may include potential well regions, implying the presence of an echo effect in its quasinormal mode oscillations.