A downhole annular barrier to be expanded in an annulus between a well tubular structure and a wall of a borehole or another well tubular structure downhole in order to provide zone isolation between a first zone having a first pressure (P 1) and a second zone having a second pressure (P 2) of the borehole, the annular barrier comprising: - a tubular part adapted to be mounted as part of the well tubular structure, the tubular part having an outer face and an inside, - an expandable metal sleeve surrounding the tubular part and having an inner sleeve face facing the tubular part and an outer sleeve face facing the wall of the borehole, each end of the expandable metal sleeve being connected with the tubular part, and - an annular space between the inner sleeve face of the expandable metal sleeve and the tubular part, - a first opening in fluid communication with the inside, - a second opening in fluid communication with the annular space, and - a bore having a bore extension and comprising a first bore part having a first inner diameter (ID 1) and a second bore part having an inner diameter (ID 2) which is larger than that of the first bore part, wherein the first opening and the second opening are arranged in the first bore part and displaced along the bore extension, and the annular barrier further comprises: - a piston arranged in the bore, the piston comprising a first piston part having an outer diameter (OD P1) substantially corresponding to the inner diameter of the first bore part and comprising a second piston part having an outer diameter (OD P2) substantially corresponding to the inner diameter of the second bore part, and - a rupture element preventing movement of the piston until a predetermined pressure in the bore is reached, characterised in that the annular barrier comprises a third opening which is in fluid communication with the annulus, and in that the piston has an initial position in which the first opening is in fluid communication with the second opening, and a closed position in which the second opening is in fluid communication with the third opening in order to equalise the pressure between the annular space and the annulus. - a tubular part adapted to be mounted as part of the well tubular structure, the tubular part having an outer face and an inside, - an expandable metal sleeve surrounding the tubular part and having an inner sleeve face facing the tubular part and an outer sleeve face facing the wall of the borehole, each end of the expandable metal sleeve being connected with the tubular part, and - an annular space between the inner sleeve face of the expandable metal sleeve and the tubular part, - a first opening in fluid communication with the inside, - a second opening in fluid communication with the annular space, and - a bore having a bore extension and comprising a first bore part having a first inner diameter (ID 1) and a second bore part having an inner diameter (ID 2) which is larger than that of the first bore part, - a piston arranged in the bore, the piston comprising a first piston part having an outer diameter (OD P1) substantially corresponding to the inner diameter of the first bore part and comprising a second piston part having an outer diameter (OD P2) substantially corresponding to the inner diameter of the second bore part, and - a rupture element preventing movement of the piston until a predetermined pressure in the bore is reached,