It is well known that there exists a Hawking-Page phase transition between a spherical anti-de Sitter (AdS) black hole and a thermal AdS space. The phase transition does not happen between a Ricci flat AdS black hole whose horizon is a Ricci flat space and a thermal AdS space in the Poincar\'e coordinates. However, the Hawking-Page phase transition occurs between a Ricci flat AdS black hole and an AdS soliton if at least one of the horizon coordinates for the Ricci flat black hole is compact. We show a similar phase transition between the Ricci flat black holes and deformed AdS solitons in the Gauss-Bonnet gravity and the dilaton gravity with a Liouville-type potential including the gauged supergravity coming from the spherical reduction of Dp branes in type II supergravity. In contrast to Einstein gravity, we find that the high temperature phase can be dominated either by black holes or deformed AdS solitons depending on parameters.
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Cai et al. (2007) studied this question.
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