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The Argument that Regulus Black is R.A.B.
Support for the theory that Regulus Black is R.A.B. has been gathered from the translation of Half-Blood Prince to other languages. In the Dutch translation of the novel, Regulus Black is called Regulus Zwarts and the initials in the locket are R.A.Z. In the Norwegian edition, Regulus Black is called Regulus Svaart, and the initials R.A.S. are in the locket, while in the Finnish translation, Regulus Black is called Regulus Musta, and the initials are R.A.M. These make the theory that R.A.B. is Sirius's brother quite plausible. Other potential candidates, such as Mr Borgin (of "Borgin and Burkes") do not translate in the same way. Also, the fact that Rowling would take an entire page of her book to explain Regulus and really create him as a detailed character appears suspicious: Rowling is not known for any great characterisation of unimportant characters, so her build-up of him without any reason would be an unusual aberration. However, it is neither confirmed nor denied whether Rowling had any communications with the translators regarding either the initials or Regulus's surname.
During the attempt to retrieve the locket with Harry's assistance, Dumbledore points out that the task could not be achieved by one person alone. Presuming Regulus is indeed R.A.B., he would have needed assistance to replace the Horcrux with the fake locket, after turning against Voldemort for any number of possible reasons. Readers have suggested that Regulus could have had the services of the Black family house-elf Kreacher. It is stated earlier in Harry Potter and the Half-Blood Prince that Regulus only survived a few days after Voldemort realised he had turned against him. However, Sirius was older than Regulus, meaning that he would be Kreacher's master before Regulus, as the elf and the house would most like go to the oldest heir. However, noting that Sirius was "erased" from his family, it would make much more sense as to why Kreacher would be Regulus's first. Whether the house and elf/writer of the will chooses its favourite heir, or whether they would consider anyone in the family their masters may be debatable, seeing as the house and elf hate Sirius.
The note suggests that the original locket would have been either destroyed or hidden away. Chapter 6 of Harry Potter and the Order of the Phoenix mentions a heavy unopenable locket in a glass case in the drawing room of 12 Grimmauld Place, the Black family home. Sirius Black was at that time clearing the house, and the locket was consigned to be thrown away. However, Kreacher was rescuing items for himself, and Mundungus Fletcher was taking items to sell. In Half-Blood Prince, Mundungus is seen with articles taken from the house, and in the company of the barman from the Hog's Head. J.K. Rowling confirmed that the barman is Dumbledore's brother Aberforth. Aberforth was described as drawing his cloak about his throat as he walked away from the scene. It is possible that he now has the locket.
A further potential clue is that the writer of the note refers to Lord Voldemort as the Dark Lord. In The Order of the Phoenix, after being scolded by Professor Snape for using "the Dark Lord's name", Harry retorts that only Death Eaters refer to him as the Dark Lord, as opposed to He-Who-Must-Not-Be-Named or You-Know-Who. This would appear to suggest that R.A.B. is, or was a former Death Eater (although since Ginny Weasley, anything but a Death Eater, referred to Harry in her sung valentine to him (in CoS) as 'The Hero who conquered the Dark Lord', Harry may have been wrong in claiming that 'only' Death Eaters use the title).
In an interview with Rowling, Emerson and Melissa (of Mugglenet and Leaky Cauldron respectively) asked if R.A.B. could be Regulus Black. Jo replied that she thought "that would be... a fine guess." Whether she is hinting that this is correct or completely shooting it down is up to interpretation.
The Argument that R.A.B. is not Regulus Black
There are, however, counter-arguments to the theory that Regulus Black is R.A.B. From what Rowling has shown readers, Kreacher is completely lacking in both the sanity and fortitude to be involved in such an arduous venture, let alone play a major role. Rowling has also given nothing to indicate that Regulus Black had the courage to drink the potion which has been seen, by its effects upon Albus Dumbledore, to cause such great pain. (Though proponents of the theory believe that it was drinking the potion that produced the state that Kreacher is now in.)
The popular theory that the 'unopenable locket' in no. 12 Grimmauld Place is Slytherin's locket, and a horcrux, is flawed: although it is indeed a heavy locket, its colour was not referred to. More importantly, Harry upon seeing it did not notice the prominent snake engraved upon it: which one would expect him to note immediately (after all, snakes in wizarding Britain seem to be very much linked to Slytherin, and Harry has a sensitivity to snakes due to his inheritance of Voldemort's power). Rowling has a history of hiding red herrings in her novels (for example, the suggestion in HBP that Nymphadora Tonks was in love with Sirius Black: she in fact proves to be in love with Remus Lupin), and it would be unsurprising if the locket were to prove so again.
The title of 'Dark Lord' has been shown not to be the exclusive preserve of (former) Death Eaters: Professor Trelawney uses the title in her two prophecies, and the indubitably virtuous Ginny Weasley uses it in her valentine to Harry Potter. One must also remember that when Harry mocks Snape with the claim that 'only Death Eaters' call Voldemort 'Dark Lord', he is still a school-student, and still has little knowledge of the wizarding world: it cannot be assumed that he has any great knowledge of the usage.
Thus far in the novels, all accounts of Regulus Black have suggested that he was a coward; Sirius Black specifically claimed that Regulus became scared of his involvement in Voldemort's organisation, and tried to escape, only to be killed. Nothing has been said to suggest that Regulus Black was brave enough, or had any inclination, to shift loyalties and damage Voldemort.
Theoretically, Black could have learned the secret of the Horcruxes, or of Voldemort's blood, etc. (if, for example, the Inferi were kept in the enchanted cave in the First War). But there has been no confirmation or denial of any (largely unfounded) suggestions of how it could have happened. Certainly, finding out the full secrets of the Horcruxes, and of Voldemort, would be a tremendous task for Regulus: who, given his birth year, can only have been out of school for around six months before his death.
Middle name
In August 2005, the Harry Potter Lexicon claimed to have been informed by a reliable source that Regulus' middle name is Arcturus.
The Lexicon claim that Regulus's second name is Arcturus has since been withdrawn, but without any explanation of the incident. However, one of the editors of that fansite has stated that he stands behind this information. He posted the following on another site (The Leaky Cauldron):
Obviously, Jo is the source of this information. When have you ever known me to post rumours as facts? It's from Jo. That doesn't mean she talked to me directly, of course, but I do know that it came from Jo.
I honestly think that Jo figures she's already told us that it's Regulus. Read the Melissa/Emerson interview. I think she would be surprised that this is even an issue.
I have asked permission to reveal who told me. If they say I can, I'll let you all know. Otherwise, feel free to take this with whatever grain of salt you need to.
Steve
—Comment posted at "The Leaky Cauldron" fan site.
Subsequently, in January 2006, the name Arcturus indeed appeared as that of one of Sirius and Regulus's ancestors in a hand-drawn sketch of the Black family tree made by J.K. Rowling herself. Therefore, it is plausible, although not confirmed in any way, that Regulus could have had Arcturus as a middle name.
The astronomical associations of Regulus are also worth considering. Regulus is a bright star in the constellation of Leo; another bright star in that constellation, close to Regulus, is Algieba. There is a less bright star, Aldhafera in the same constellation. Notably, Algieba and Regulus are two of five stars in Leo which can be seen even during bad light pollution: light amid the darkness (and if Regulus was a 'good' person in the midst of evil death eaters, he would be 'light amid the darkness').
However, it has also been noted in the books (and the aforementioned family tree) that Regulus had an uncle whose name was Alphard, after whom some speculate that Regulus may have instead been named. The name could be Alphard, since middle names are often family members of the same gender.
Nevertheless, if Regulus was not R.A.B., then his middle name could, essentially, begin with any letter, making all "A" name theories not applicable.