Energetic processes and thermodynamic analysis of the spinning Kiselev black hole with cloud of strings

Here we study the impact of the string clouds, the quintessence dark energy and other spacetime parameters on the center -of -mass energy, Penrose -process and thermodynamic properties of a stationary black hole solution of the Einstein field equations. We observe that the three distinct horizons i.e the Cauchy horizon, the event horizon and the cosmological horizon exist when the spin parameter a of the black hole is less than its extremal value a E . Interestingly we see that the infinite redshift surface of the black hole is not much sensitive to the quintessence parameter y. It is sensitive to the parameter a and it increases as the parameter a increases. Further, we notice that an increase in the string cloud parameters b, quintessence parameter y and a make the radius of the ergosphere of the black hole larger. We also notice that a rise in the parameter a makes the innermost stable circular orbits (ISCO) smaller and for an increase in the parameter b and y the ISCO becomes larger than that for the Kerr spacetime. For the center -of -mass energy of the spinning black hole with quintessence and cloud of strings we observe that it can be arbitrarily high only for the extremal case of the black hole for a specific range of values of the angular momentum of the colliding particles. We notice that the Penrose -process is more efficient for smaller values of the string cloud parameter b and the parameter y has no significant impact on this process. Moreover we see that an increase in the parameters b, y and a cause the Helmholtz free energy to increase and opposite is true for the temperature of this type of rotating black hole. We learn that the area and entropy of the black hole are also depend on the parameters b, y and a, and their effect make the entropy smaller. Interestingly we find a range of the horizon radius for the thermodynamic stability of the black hole. To get more information about the thermodynamic quantities of the rotating black hole with quintessence and cloud of strings, we plot them for different ranges of the spacetime parameters.