Quasinormal modes in nonlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math> models in the Eddington inspired Born-Infeld gravity

In this paper we explore properties of the spacetime of the monopole in nonlinear $\ensuremath{\sigma}$-models in the Eddington inspired Born-Infeld gravity. Particularly, we examine the radii of characteristic circular orbits of the test particles such as the circular null geodesics, marginally bound and stable circular orbits as a function of the spacetime parameters. Furthermore, we explore the dynamics of the massless scalar field. To enhance the precision of calculations, we employ multiple methods, including the WKB (Wentzel-Kramers-Brillouin) approximation, asymptotic iteration, and continued fractions methods. Our calculations demonstrate that the scalar field within the field of the monopole under examination remains stable against scalar perturbations. Notably, variations in the monopole parameter influence the longevity of the damping time of perturbations, with smaller damping rates prolonging their existence.

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