Einstein–Gauss–Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein–Gauss–Bonnet gravity in various spacetime dimensions with both positive and negative coupling constant $$\alpha $$
α
. By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $$\alpha >0$$
α
>
0
, in $$D\geqslant 6$$
D
⩾
6
cases, the black holes will be completely evaporated in a finite time, which resembles the Schwarzschild-AdS case in Einstein gravity. While in $$D=4,5$$
D
=
4
,
5
cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $$\alpha >0, D=4,5$$
α
>
0
,
D
=
4
,
5
will solve the terminal temperature divergent problem of the Schwarzschild-AdS case. For $$\alpha <0$$
α
<
0
, in all dimensions, the black hole will always spend a finite time to a minimal mass corresponding to the smallest horizon radius $$r_{min}=\sqrt{2|\alpha |}$$
r
min
=
2
|
α
|
which coincide with an additional singularity. This implies that there may exist constraint conditions to the choice of coupling constant.
We discuss the P -V criticality and phase transition in the extended phase space of Born-Infeld AdS (BI-AdS) black hole surrounded by quintessence dark energy, where the cosmological constant Λ is identified with the thermodynamical pressure P . Comparing with Van der Waals(VdW)-like SBH/LBH phase transition of Born-Infeld AdS (BI-AdS) black hole, we find that the BI-AdS black hole surrounded by quintessence dark energy possesses lower critical temperature because of parameter a > 0, even disappears since the parameter a taking enough large values leads to Tc ≤ 0. Moreover, the interesting thermodynamic phenomenon of reentrant phase transition (RPT) are also observed, and the quintessence dark energy plays a similar role in this RPT.
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