Epicyclic oscillations, particle collisions, emission energy and thermal fluctuation around a black hole with de-sitter core

This study tested the geometric structure and dynamic behavior of particles around a non-rotating black hole (BH) featuring a de Sitter core. We derive the space-time metric and analyze key features such as the lapse function, effective potential, innermost stable circular orbits (ISCOs), and particle trajectories. The Hamiltonian framework reveals that the de Sitter core radius R significantly influences particle dynamics: a larger R shifts the effective potential minima closer to the horizon, enhances the attractive effective force and marginally impacts the ISCO radii. Numerical solutions of motion demonstrate modified trajectories compared to Schwarzschild BHs, with a higher center of mass energy (CME) near the horizon for larger R. Harmonic oscillation frequencies, periastron precession, and thermodynamic properties, including temperature, specific heat, and Hawking radiation emission, are quantified. Thermodynamic stability is tested for specific parameter ranges, with the temperature decreasing as R increases. Our results explain the relation between the de Sitter core and gravitational dynamics, providing insight into the stability and energy properties.