Universal thermodynamic extremality relations for charged AdS black hole surrounded by quintessence

Abstract: The perturbation correction of general relativity has obtained the general relationship between entropy and extremality. The relation was found to exactly hold for the charged AdS black hole, and extended to the rotating and massive gravity black holes. In this paper, We confirm the universal relation for the four dimensional RN-AdS black hole surrounded by the quintessence, and find a new extremality relation between black hole mass and the normalization factor $a$ related to the density of quintessence. Besides, we also find that when the black hole entropy increases, the correction constant is negative, the black hole mass and the mass-charge ratio decreases, hence this black hole displays WGC-like behavior. Moreover, we derive the general relationship on nonlinear electrodynamic source couples to AdS spacetime with quintessence field. We find another new extremality relation between black hole mass and the magnetic monopole charge $\beta$.