摘要
By looking at the Lovelock theorem one can infer that the gravity model given by[1]cannot be applicable for all types of 4D Einstein–Gauss–Bonnet(EGB)curved space-time.The reason for this is that in 4D space-time,the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics.Hence,the authors of[2]presented an alternative consistent EGB gravity model instead of[1]by applying a break-of-diffeomorphism property.In this work,we use the alternative model to produce a de Sitter(dS)/Anti-de Sitter(AdS)black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings.Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the d S sector but not in the Ad S background.From this,we infer that the black hole participates in the small-to-large black hole phase transition in the dS background,while it exhibits a Hawking–Page phase transition in the AdS background.In the latter case,an evaporating black hole eventually reaches an AdS vacuum space because of its instability.
