Quasibound states of scalar fields in the consistent 4D Einstein–Gauss–Bonnet–(Anti-)de Sitter gravity

We examine the interaction between massless scalar fields and the gravitational field generated by a black hole solution that was recently obtained in the consistent well-defined 4-dimensional Einstein–Gauss–Bonnet gravity with a cosmological constant. In order to do this, we calculate quasibound state frequencies of scalar fields for the spherically symmetric black hole in the consistent 4-dimensional Einstein–Gauss–Bonnet–de Sitter and Anti-de Sitter theories. The expression for the quasibound states is obtained by using the polynomial condition associated to the Heun functions, and their values are overdamped. We also demonstrate the stability of the systems.