Barrow entropy effects on thermodynamics and quasi-periodic oscillations around a Frolov black hole

This study investigates the geometric structure, particle dynamics, and thermal properties of the non-rotating Frolov black hole. We analyze the black hole geometry and derive the effective potential governing the motion of the test particle, showing the influence of the BH charge Q and the parameter α on the motion of the particle. Using the Hamiltonian formalism, we determine the angular momentum, energy, and innermost stable circular orbits of the particles, demonstrating that increasing Q and α shifts the innermost stable circular orbit radii closer to the horizon and reduces the stability of the orbit. The effective force acting on the particles becomes more attractive with higher Q and α . Harmonic oscillatory motion around stable orbits reveals distinct radial, latitudinal, and axial frequencies, which diminish near the horizon for larger Q and α . Periastron precession rates similarly decrease with these parameters. The center of mass energy near the horizon escalates with Q and α , suggesting enhanced energy extraction efficiency. We also study the black hole thermodynamics, and found that the black hole exhibits a positive Hawking temperature and entropy, while the specific heat analysis indicates phase transitions and regions of stability dependent on Q , α , and the Barrow entropy parameter. The emission energy rates decrease as Q and α increase. Our results generalize the Schwarzschild black hole case ( Q = α = 0 ) and provide critical insights into the interplay between charge, space-time structure, and thermodynamic behavior in Frolov black hole geometries.