Pulsating string solution and stability in two parameter $\chi$-deformed background

TL;DR

This paper studies pulsating string solutions and their stability in a two-parameter $hi$-deformed background, deriving energy relations and analyzing perturbations to understand their behavior in deformed geometries.

Contribution

It introduces a detailed analysis of pulsating strings in two-parameter deformed backgrounds, including energy relations and stability criteria, extending previous single-parameter studies.

Findings

Derived energy and oscillation relations for short strings in deformed backgrounds.

Formulated the first-order perturbation equations for pulsating strings.

Analyzed stability of solutions in one-parameter deformed backgrounds.

Abstract

In this paper, we investigate pulsating string solutions within the context of a two-parameter $\chi$-deformed $\mathcal{R} \times S^2$ background. We derive the energy and oscillation number relation for the deformed $\mathcal{R} \times S^2$ in a short string limit. Additionally, we derive the first-order perturbation equation for a 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 $\mathcal{R} \times S^2$ and $AdS_3$ background by setting one of the deformation parameters to zero.