... replaces the WT's three oaths by a triad of Oaths of their own, which they also swear on the Oath Rod (probably the Tower's own, Galina implied as much by omission but it's not fully confirmed). That's how the Black has managed to remain invisible among the bound sisters. It's been speculated (but again it's not confirmed), that it takes the same number of active Oaths taken on the OR to achieved the same look and cut your lifespan by the same amount of years or percentage, thus it would be the reason why the BA also swear three oaths, so no subtle difference about them could eventually be noticed (not as perfect agelessness or a tendency to live a few decades more than the most long-lived AS and so on).