The Hawking–Page (HP) phase transitions of the anti-de Sitter black holes in the extended phase space are studied in a novel four-dimensional Einstein–Gauss–Bonnet (4EGB) gravity, which is proposed by rescaling the Gauss–Bonnet (GB) coupling constant $\alpha \to \alpha ∕(d-4)$ in $d$ dimensions and redefining the four-dimensional gravity in the limit $d\to 4$. The GB term shows nontrivial contributions to both black hole mass and entropy simultaneously, and decreases the HP phase transition temperature $T_{\mathrm{HP}}$. Moreover, the HP phase transitions can occur only within a range of pressure in the 4EGB gravity. For the charged black holes, $T_{\mathrm{HP}}$ also decreases with the electric potential in the grand canonical ensemble. A general discussion of the HP phase transitions in the Einstein, GB, and 4EGB gravities is also presented.

在新型的四维爱因斯坦-高斯-贝内特（4EGB）引力中研究了反相位Sitter黑洞在扩展相空间中的霍金-佩奇（HP）相变，该问题通过重新调整高斯-贝内特（ GB）耦合常数 $\alpha \to \alpha ∕（d-4）$ 在 $d$ 尺寸并在极限中重新定义三维重力 $d\to 4$。GB项同时显示了对黑洞质量和熵的重要贡献，并降低了HP相变温度${Ť}_{\mathrm{生命值}}$。此外，HP相变只能在4EGB重力下的压力范围内发生。对于带电的黑洞，${Ť}_{\mathrm{生命值}}$大正则合奏中的电势也随电势下降。还介绍了在爱因斯坦，GB和4EGB重力下的HP相变的一般讨论。