Generalised Hayward spacetimes: Geometry, matter and scalar quasinormal modes

TL;DR

This paper generalizes Hayward spacetimes using the Damour-Solodukhin approach, exploring a wide class of geometries including black holes and wormholes, and analyzes their scalar quasinormal modes to assess their potential as black hole mimickers.

Contribution

We extend the Hayward spacetime by applying the DS deformation, creating a broad family of geometries and studying their properties and scalar quasinormal modes.

Findings

Identified new and known spacetime geometries within the generalized class.

Analyzed how quasinormal modes vary with metric parameters.

Suggested these geometries can mimic black hole signals.

Abstract

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 realised 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 generalise the Hayward spacetime by applying the Damour-Solodukhin (DS) prescription. Recalling the DS suggestion of a deformed Schwarzschild spacetime where $g_{tt} = -\left (1-\frac{2M_1}{r}\right )$, $g_{rr} = \left (1-\frac{2M_2}{r}\right )^{-1}$ and $M_1\neq M_2$, we propose a similar deformation of the Hayward geometry. The $g_{tt}$ and $g_{rr}$ in the original Hayward line element remain functionally the same, {\em albeit} mutations 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.