The vulnerability window is the time period for when sovereignty structures are vulnerable to disruption via the Entosis Link. These are otherwise invulnerable and cannot be captured or destroyed at all. Alliances can select the midpoint of their vulnerability window, which is called their "Default Sovereignty Vulnerability Time", or prime time (see below).
The Activity Defense Multiplier determines the full duration of the vulnerability window so it can potentially change on daily basis (because of shifting System Indices), but the selected vulnerability time point around which the vulnerability window opens will always stay the same. To determine what the full duration of the vulnerability window is, simply divide 18 hours by the defense multiplier so it can be 18 hours at most with the lowest defense multiplier and 3 with the highest.
The exact duration of the vulnerability window is locked in at the selected vulnerability time the day before. Changes to the defense multiplier that occur after the vulnerability window is locked in will not affect the duration following vulnerability period but will instead affect the duration when it is next locked in.
Structures that are claimed during the alliance vulnerability window will become vulnerable immediately for the remaining duration of the window.
If a structure is already under attack when the vulnerability window expires then it goes into overtime. The structure remains vulnerable indefinitely if no one is actively trying to conquer or defend it, until conquered or defended by either side.
Default Sovereignty Vulnerability Time
The Default Sovereignty Vulnerability Time can be set by the Alliance Executor Corporation and requires a specific corp role (currently Director). The vulnerability window is centered on the selected vulnerability time and scales in both directions. For example, if the vulnerability window is 4 hours and prime time is set to 16:00 then the vulnerability window will be from 14:00 to 18:00.
Once the prime time has been changed, the change will take effect the following day rather than immediately.