A Study on the Effect of Quintessence on the Thermodynamics of Perturbed Schwarzschild Black Hole

Phenomena such as black hole (BH) growth, Hawking radiation and gravitational waves are captivating not only in changing spacetime’s curvature but also in affecting the thermodynamics characteristics of the sources with respect to time. The current study aims at exploring the effects of time and quintessential dark energy on the thermodynamical properties of the perturbed Sch. BH spacetime. A technique, based on the introduction of general time conformal factor, i.e., e^ϵμ (t) , is employed, which allows us to rescale the energy context of spacetime. Employing the Lagrangian to the perturbed spacetime, the Noether symmetry equation is acquired, which subsequently yields a set of 19 partial differential equations (PDEs). By solving these PDEs, we get the required perturbed Sch. BH spacetime with their Noether and approximated Noether symmetries along with their conservation laws. Additionally, calculation of the spacetime event horizon as a function of time t is worked out. Meanwhile, the same effect is studied as well as graphically analyzed on pressure, surface gravity, Hawking temperature, and volume of time conformal quintessential Sch. BH.