Investigation on the stability and quantum phase transition of the charged rotating Kiselev Black Hole embedded in Quintessence field with quantum fluctuation of entropy

Abstract

Immediate local impacts of cosmic acceleration upon a rapidly rotating black hole are very interesting in recent studies. In this paper, the stability of a rapidly rotating black hole and the minimum value of the ratio between the black hole’s angular momentum to it’s mass which ensures the stability, are investigated simultaneously. Also, two modern forms of uncertainty relations are proposed by enhancing the usual Heisenberg algebra with superior terms, in order to supervise on thermodynamic properties of the rotating black hole. An asymptotically flat Kiselev black hole solution, cultivated by quintessence field is chosen for this purpose. The local shifts in spacetime geometry next to the rotating black hole can be resolved from a modified metric, occupying the surrounding spacetime of the black hole. The angular momentum of a rotating black hole depends on the rate of change in acquiring mass by it. On the other hand, at the same time, due to the effect of the quintessence field, there exists repulsive gravitational force inside the black hole. So, there is an uncertainty in the position of innermost stable circular orbit as well as radius of the rotating black hole. This uncertainty is also investigated in our work. Relying on two new forms of uncertainty principle, the modified thermodynamic variables like black hole’s Hawking temperature, heat-capacity, entropy at the black hole’s event horizon, etc. are computed under rotation. Quantum corrections of black hole’s Hawking temperature, entropy, free-energy, etc. are also explored. Further, quantum corrected heat capacity of the rotating black hole is studied and also thermal stability is inquired. The existence of transitions of phase in case of a rapidly rotating black hole are also found out. Again, quantum corrected entropy of black hole contains logarithmic terms and their effects on thermal stability of the rotating black hole are also discussed. Modifications in the mass-temperature, specific heat, etc. of a rotating black hole are also presented according to the modified extension parameters.