Before Titans were trying to eat humanity or demons devouring entire families, there was a boy with a death note. Death Note is a widespread psychological horror anime that incorporates themes of God, justice, and death. Fans of the series couldn't get enough of Light Yagami and the apple-loving Shinigami Ryuk. It was no surprise that at the end of this epic show, Light was defeated and killed, but due to the OVA Death Note Relight 1 & 2, there's a theory that Light didn't die.
The two movie-length OVA's, Death Note Relight 1: Visions of a God and Death Note Relight 2: L's Successors, cover the original anime's events. A couple of changes had been made to the first film, mainly shortening the original sense to fit into the film. Though the first film is the most faithful to the original anime, Light is bored of the world, discovers the death vote, and takes justice into his own hands as Kira. In the second film, more changes have been made, specifically to Near's discovery of Light and Mikami's actions as Kira. With these changes to the original anime and the introduction of a new Shinigami, some fans believe it's a reality where Light was reincarnated as the unknown God of Death.
Light's Reincarnation
Reincarnation isn't an unusual element to find in anime, and it appearing in Death Note isn't impossible. When first discovering the death note, Ryuk explains to Light that those who use a death note can never go to heaven or hell after they die. For Light, this was not a concern since Gods don't die. Considering this, maybe those who have used a death note become Shinigami. This also supports what Ryuk meant when stating that Light had something to look forward to after his death.
There are also points regarding the unnamed Shinigami's appearance. The supposed Ligh Shinigami wears a coat similar to the one Light did the day he died, with a red tie wrapped around its foreheads, identical to the one Light wore for his school uniform. Fans had also pointed out that the Shinigami has a limp, possibly because Light was shot in the leg before he died. Even with all this evidence, some don't fully believe that Light was reincarnated.
Unlike Light, this Shinigami is wearing goggles. This is a staple of Matt, not Light. Could this mean that the Shinigami is Matt? Probably not because a Shinigami similar to the one in the OVA can be seen in the manga while Light is still in school. Ruling out Light and Matt as the supposed Shinigami. There are also the facts that Light is shorter than the unnamed Shinigami, and it's hard to imagine Light carrying a large bone ax in his next life.
Two Realities, One Shinigami Realm
Arguments will continue to go back and forth on this theory, and in reality, viewers will likely never get a concrete answer. Light reincarnating wasn't the purpose of the show. It's watching Light Yagami, a bored high schooler who thinks he can change the world transform into a monster. What started as a misguided dream to free the world of crime transformed into Light wanting to be an unstoppable God. Along the way, people were killed who were innocent, and eventually, Light was extinguished.
Then again, theorizing that the psychotic monster that is Light Yagami has been granted new life as a Shinigami is both frightening and expected. There is no better job for Light than one of a Death God. So, assuming Light did reincarnate, how could his Shinigami appear simultaneously as he was in high school? Well, Ryuk makes it clear that the world of the Shinigami and Earth are two different realms. Perhaps time and space work differently in the Shinigami realm, allowing the unnamed Shinigami to appear on Earth simultaneously as Light.
If Shinigami's can appear on Earth at any time, who's to say that the OVA isn't an alternate reality. That Ryuk was telling the story of the Light that was reincarnated. This could be why he addresses Light by name at the end of Death Note Relight 1: Visions of a God because Ryuk knew who he was talking to. Considering these hypothetical events, the Light in the anime might not have been reincarnated; instead, his soul was stuck in limbo.
All of this would definitely make the already complex world of Death Note even more intricate, but of course, these are all theories. At the end of it all, the show is a fantastic representation of psychological horror and the lengths man will go for God-like stature. Anime fans will continue to reference and enjoy the world of Death Note, even if Light never became a Shinigami. Except how did that unnamed Shinigami know Ryuk liked apples?