Barrow entropy effects on thermodynamics and QPOs of a quintessence surrounded Frolov black hole model

This research examines the dynamics and thermodynamics of a non-rotating Frolov black hole (BH) surrounded by a quintessence field, described by the parameters $Q$ (charge), $\alpha$ (Hubble length) and $\beta$ (quintessence coupling). In addition, the space-time structure, analyzed through the lapse function $h\left(r\right)$, reveals that increasing $Q$, $\alpha$, or radial distance $r$ enhances $h\left(r\right)$, while $\beta$ exerts a negligible influence on the horizon radii. The particle dynamics near the BH is governed by an effective potential $V_{eff}$, angular momentum $L$, and a specific energy $E$, which delineates stable and unstable orbits. The innermost stable circular orbits (ISCOs) contract with increasing $Q$ and $\alpha$, but expand with $\beta$, reflecting competing gravitational and quintessence-driven effects. Harmonic oscillations display unique radial, latitudinal, and orbital frequencies, which are redshift for observers at a distance, whereas periastron precession decreases for greater $Q$ and $\alpha$. From a thermodynamic perspective, the BH shows positive mass and temperature throughout various parameter ranges, indicating global stability. Heat capacity anomalies and the swallowtail patterns of Gibbs free energy indicate phase transitions, with transitions from stable to unstable relying on $\alpha$, $Q$, and $\beta$. Energy emission rates decrease as the parameters increase.