Thermodynamics and particle dynamics around a regular black hole admitting the limiting curvature condition

This paper investigates the thermodynamic and particle dynamics features of a regular black hole in the case of the limiting curvature condition. We begin by examining the metric function $f\left(r\right)$ for a regular black hole that admits a limiting curvature condition, where the length parameter l and the black hole mass M. In the case of the Schwarzschild metric when $l=0$, offering a reference point for comparison. According to the study, a more compact event horizon is indicated by a drop in the horizon radius $r_h$ as l increases. We investigate the effects of thermal fluctuations on the thermodynamic parameters, such as the Hawking temperature, entropy, and specific heat. The Gibbs free energy and energy emission rates are also analyzed to show the black hole's stability and phase changes. We also study particle motion near the black hole, with particular attention to photon orbits, innermost stable circular orbits (ISCO), and the effective potential. Analysis of the red and blue shifts of photons released by orbiting particles shows how the length scale parameter l affects the frequency shifts that are seen. In this context, we show the oscillations of massive particles around circular orbits, deriving the fundamental frequencies associated (quasi-periodic oscillations (QPOs) and exploring various QPO models). The results explain the thermodynamic and dynamic behavior of regular black holes under limiting curvature, revealing insights into their stability, phase transitions, and observational signatures.