Black holes in degenerate Einstein Gauss-Bonnet gravity: can QNMs distinguish them from GR?

For the first time, we study the quasi-normal modes(QNMs) of massless scale fields propagating in spacetimes with zero metric determinant. In this context, we work with asymptotically flat solutions to degenerate Einstein-Gauss-Bonnet (EGB) theory introduced in [ JCAP 02 (2022) 020]. This solution has two distinct branches akin to Einstein Gauss-Bonnet(EBG) gravity. However, unlike the EBG solutions, both the branches of dEGB are well-defined asymptotically. The negative branch solutions from both theories are equivalent under the identification of certain parameters. We provide constraints on the Gauss-Bonnet coupling parameters, which result in black hole spacetimes, and study the behaviour of a propagating scalar field through the computation of QNMs. Finally, we compare the time domain evolution of the scalar field in the background of these black holes with their GR counterparts.