Pulsating string solution and stability in two parameter χ-deformed background

Abstract

In this paper, we investigate pulsating string solutions within the context of two parameter χ-deformed $$ \mathcal{R} $$ R × S2 background. We derive the energy and oscillation number relation for the deformed $$ \mathcal{R} $$ R × S2 in short string limit. Additionally, we derive the first order perturbation equation for pulsating string in this specific background. As a special case of the two parameter deformed background, we examine the stability of the pulsating string solution in one parameter deformed $$ \mathcal{R} $$ R × S2 and AdS3 background by setting one of the deformation parameters to zero.