The eyes of the Sage of the Six Paths, Hagoromo Ōtsutsuki, are known to be the supreme dōjutsu.
They derive from the eyes of Kaguya Ōtsutsuki, the Rabbit Goddess, who possessed the Rinne-Sharingan and the Byakugan.
The Rinnegan was introduced into the narrative in chapter 238 by Pain.
From that point on, the Rinnegan went through various changes. It started with a circular motion the size of the iris and ended as we know it today.
This is the current design portrayed by Pain in chapter 428.
According to the third databook, the Rinnegan is a type of Kekkei Genkai. This means that it can only be passed down within a bloodline.
Third databook, page 313.
This is also known as a Bloodline Limit, like the Sharingan or the Byakugan.
However, in the case of its original user, Hagoromo, it is classified as a Kekkei Mōra, a special bloodline branch exclusive from the Ōtsutsuki Clan.
Kaguya’s Byakugan and Hagoromo’s Rinnegan are the only known Kekkei Mōra in Naruto.
Kaguya possessed the Rinne-Sharingan, a Kekkei Mōra combination of the Rinnegan and the Sharingan.
This eye is exclusive to Kaguya.
Sasuke Uchiha does not possess a Rinne-Sharingan.
Hagoromo was the first person to awaken the Rinnegan as the variant we know today. The anime filler of Naruto Shippūden 462, it is explained that Hagoromo was born with the Byakugan, which later developed in Sharingan, MangekyōSharingan, and finally in the Rinnegan.
However, this is only a filler that could serve as a means of contextualization.
After him, the Rinneganhas only been awakened naturally by Madara Uchiha. A feat only he could do.
In chapter 670 of the manga, Naruto Uzumaki meets the Sage of Six Paths.
And spots the Rinnegan in his eyes.
He narrates the story of his two sons Indra and Ashura, which holds a strong parallelism with Sasuke and Naruto, as well as with Madara and Hashirama.
He explains how he passed down his legacy to the younger brother and left the responsibility with him instead of sharing it between both brothers.
This angered the eldest brother, who was considered the most suitable inheritor of the power of the Sage of Six Paths. This developed in a sibling dispute.
The circle of Reincarnation is introduced into the narrative.
Indra and Ashura lived enough to create their own families.
Indra became the progenitor of the Uchiha Clan and Ashura became the progenitor of the Senju and Uzumaki Clans.
According to the fourth databook, the descendants of Indra, the Uchiha, inherited the power of Yin Release and the descendants of Ashura, the Senju, inherited the power of Yang Release.
Fourth databook, page 226.
Sasuke and Naruto have affinities to these two types of release.
In chapter 671, Hagoromo says that he can see Ashura’s chakra flowing inside Naruto, as well as his elder son Indra’s flowing inside Sasuke.
This detail is very important.
Hagoromo says that, before Sasuke and Naruto, the previous reincarnates of Indra and Ashura were Madara Uchiha and Hashirama Senju, both individuals being direct descendants of the brothers.
This is the key to awakening the Rinnegan.
A few panels later, he explains how Madara gained the powers of the Rinnegan. The Rinnegan is only awakened by merging Indra and Ashura’s chakra together, which, together, recreate the chakra of Hagoromo.
Not combining Uchiha and Senju blood or chakra.
Madara, who never learnt that he was a reincarnate, transplanted Hashirama’s (Ashura’s reincarnate) flesh into a wound after their fateful fight.
By the end of his life, he awakened the Rinnegan. He explains this in chapter 606.
It takes several years to complete this transformation.
Madara awakened the eye of the myth of the Sage of Six Paths. For example Ibiki Morino in chapter 425 explains that these eyes were possessed by the father of all Shinobi.
However, there is another way to obtain the Rinnegan: directly from Hagoromo.
Hagoromo bestowed Sasuke his Rinnegan in the left eye only in chapter 673.
Like I said before, even if Sasuke’s Rinnegan looks like Kaguya’s, it is not a Rinne-Sharingan. Kaguya possessed the Kekkei Mōra Rinne-Sharingan.
Sasuke has the Kekkei Genkai Rinnegan given by Hagoromo.
End.
In order to awaken the Rinnegan, one must possess chakra from Indra and Ashura Ōtsutsuki. If somebody doesn’t have that requirement, they won’t achieve the Rinnegan, no matter if they mix blood from the Senju and Uchiha.
I have seen many fans say that Sarada Uchiha will be able to obtain a Rinnegan if she has access to Senju blood from Naruto or Hashirama’s cells, or that she marries Boruto Uzumaki their children will possess it.
This is simply impossible. She does not have Indra’s chakra, the only thing that connects her to him is the Uchiha name, which descends from Indra.
The last reincarnations to ever exist, as the cycle of “sibling squabbling” ended with Sasuke and Naruto, are those two.