Hawking-Page transition in anti-de Sitter massive gravity with noncompact spatial boundary

In gauge-gravity duality, the Hawking-Page (HP) process plays the important role of representing a confined-deconfined phase transition. For spaces that are asymptotically anti–de Sitter with a planar spatial boundary, there is no HP transition, unless some infrared energy scale is introduced. Massive gravity theories have been applied in the context of holography in order to represent systems with momentum dissipation. In this work, we study the HP transition for massive gravity in an asymptotically anti–de Sitter space with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi mathvariant="double-struck">R</a:mi> <a:mi>n</a:mi> </a:msup> <a:mo>×</a:mo> <a:mrow> <a:msup> <a:mrow> <a:mi mathvariant="normal">S</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msup> </a:mrow> </a:math> boundary. It is shown that the graviton mass term produces an HP transition at a finite critical temperature.