Generalized Hayward spacetimes: Geometry, matter, and scalar quasinormal modes

Bardeen's 1968 idea of a regular black hole spacetime was revived by Hayward in 2006 through the construction of a new example of such a geometry. Later it was realized by Neves and Saa, that a wider, two-parameter class exists, with Bardeen and Hayward spacetimes as special cases. In this article, we revisit and generalize the Hayward spacetime by applying the Damour-Solodukhin (DS) prescription. Recalling the DS suggestion of a deformed Schwarzschild spacetime where gₓₓ=- (1-2M₁r), gₑₑ= (1-2{M₂r) }^-1 and M₁M₂, we propose a similar deformation of the Hayward geometry. The gₓₓ and gₑₑ in the original Hayward line element remain functionally the same, albeit with changes introduced via differently valued metric parameters, following the DS idea. This results in a plethora of spacetime geometries, known as well as new, and including singular black holes, wormholes or regular black holes. We first study the geometric features and matter content of each of such spacetimes in some detail. Subsequently, we find the scalar quasinormal modes corresponding to scalar wave propagation in these geometries. We investigate how the real and imaginary parts of the quasinormal modes depend on the values and ranges of the metric parameters used to classify the geometries. Finally, we argue how our results on this family of spacetimes suggest their utility as black hole mimickers.