Board Thread:Theories and Speculation/@comment-25712820-20150117183302/@comment-5413572-20150117195355

I doubt very much that Boruto will get any kind of dojutsu- it wouldn't seem to fit themeatically.

Now, that said, the Rinnegan is awakened by recombining Asura and Indra's chakras. The Tenseigan, meanwhile, seems to be awakened by combining the chakras of the Hyuga and Otsutsuki (based on new details given in | this thread). In other words:

Rinnegan = Asura + Indra (Sharingan) Tenseigan = Otsutsuki + Hyuga (Byakugan)

Given that they're the children of Naruto and Hinata, Boruto and Himawari's heritage would thus be:

Asura + Hyuga (Byakugan) = ????????

So, it's entirely possible that a unique mixture of Hagaromo's and Hamura's chakras will result in these two, awakening a new dojutsu altogether. This could also explain why both of them lack the Byakugan, as well as their teal-colored eyes. (Although the former could be a recessive or patriarch-passed trait, as the wiki suggests; and the latter could be a result of Hinata's white eyes- eye color is a polygenic trait, and combinations of the parents' eye colors in the children is thus possible. Still the possibility exists.)