Effect of dark energy on Hawking-Page transition

It is well known that there exists a Hawking-Page (HP) transition between Schwarzschild-AdS (SAdS) black hole and the thermal AdS vacuum. In this paper, we study a similar phase transition under the effect of dark energy, namely HP transition of AdS black hole surrounded by quintessence dark energy. It is shown that there always exists a HP transition between the quintessence AdS (qAdS) black hole and the thermal AdS vacuum. In contrast to Einstein gravity, we find that the high temperature phase can be dominated either by the qAdS black hole or the thermal AdS vacuum depending on the constants of quintessence dark energy, including the constant omega(q) for the equation of state and the constant a for the density of quintessence. The a - omega(q) parameter space for physical HP transition is presented. Besides, a always diminishes the HP temperature; while.q enlarges the HP temperature when -1 < omega(q) = - 2/3, and omega(q) diminishes the HP temperature when - 2/3 <= omega(q) < - 1/3. Furthermore, the HP temperature of qAdS black hole is always smaller than that in Einstein gravity, while the a = 0 limit reduces to HP transition in Einstein gravity. (C) 2020 Elsevier B.V. All rights reserved.