Reentrant Hawking–Page phase transition of charged Gauss–Bonnet-AdS black holes in the grand canonical ensemble

Abstract In this paper, we study the reentrant Hawking–Page transition in the grand canonical ensemble of Gauss–Bonnet AdS spacetime. We find that the four-dimensional Gauss–Bonnet hyperbolic AdS black hole always has a reentrant Hawking–Page transition in the range of electric potential $$0&lt;\Phi &lt;\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>Φ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , accompanied by the appearance of the triple point. However, once the potential exceeds a certain upper limit $$\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:math> , i.e. $$\Phi &gt;\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the Hawking–Page transition disappears. In the spacetime of five and higher dimensional Gauss–Bonnet hyperbolic AdS black hole, the reentrant Hawking–Page transition is solely observed to occur when the electric potential $$\Phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Φ</mml:mi> </mml:math> lies between two specific thresholds ( $$\Phi _{c}&lt;\Phi &lt;\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:mi>Φ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). In scenarios where the electric potential is below $$\Phi _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> ( $$\Phi &lt;\Phi _{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> ), only the standard Hawking–Page transition as in the the Einstein gravity is observed. Similar to the four-dimensional case, the Hawking–Page transition is negated when the electric potential exceeds $$\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:math> ( $$\Phi &gt;\Phi _{tr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Φ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>Φ</mml:mi> <mml:mrow> <mml:mi>tr</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). We give the coexistence line, the triple point and critical point of the Hawking–Page transition in the phase diagram of the Gauss–Bonnet hyperbolic AdS black hole. The observed reentrant Hawking–Page transitions and triple points in the context of Gauss–Bonnet hyperbolic AdS black holes may correspond to the phase transitions and triple points in QCD phase diagrams, following the spirit of the AdS/CFT correspondence. To be a complete research, the Hawking–Page transition of d-dimensional charged spherical Gauss–Bonnet-AdS black hole in the grand canonical ensemble is also study in the Appendix, for which there exists a standard Hawking–Page transition with the transition temperature depending on the Gauss–Bonnet constant $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> .