Particles dynamics with QPOs and thermodynamics features around a deformed anti-de sitter Schwarzschild black hole

Abstract We explore the dynamics of test particles around a deformed anti-de Sitter Schwarzschild black hole and analyze the influence of model parameters on particle motion. Using the effective potential technique, we examine the stability of equatorial circular orbits. We obtain the analytical expressions for the energy and angular momentum of test particles, along with the innermost stable circular orbits and the effective forces acting upon the test particles. We also probe the epicyclic oscillations of test particles close to the equatorial plane and further evaluate analytical expressions for radial, vertical, and orbital frequencies, including the periastron precession frequency. Additionally, we study the thermal characteristics of the black hole, investigating its Gibbs free energy, emission energy, and check the influence of other thermodynamic properties on the black hole model. Our findings indicate that the model parameters M , $$ \Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> , $$ \alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and $$ \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> considerably affect both the particle motion including epicyclic oscillations and the thermodynamic behavior.