The Arkenstone, as described in The Hobbit, was a fantastic jewel found in the heart of the Lonely Mountain. It gave off it’s own light, but would become even more brilliant when reflecting the light of something else. It was an heirloom of Thorin’s family, and was therefore highly coveted.
Now, there is a very interesting theory among some fans that the Arkenstone was actually one of the silmarils (specifically the one Maedhros threw into the fiery chasm in the earth.) Here are the main arguments supporting this theory, and any holes in such arguments.
Do to the major changes the world underwent after the War of Wrath, when Beleriand was sunk and such, or maybe even due to flowing magma under the surface of the earth, the silmaril/Arkenstone could easily have moved from Beleriand to the Lonely Mountain. The mountain was likely once a volcano (being a singular mountain in the middle of a plain), which would explain how the stone worked its way closer to the surface. (It’s unclear in any of the geology/geography of our world stands up in Middle Earth, though.)
The Arkenstone’s description sounds very much like a silmaril. The silmarils gave off the light of the Two Trees of Valinor, but also fed off of light, becoming much more brilliant when reflecting light from something else. However, while the silmarils shined brightly, the Arkenstone is described as giving off more of a pale glow. Some fans suggest that, being deprived of any light for so many years while trapped under the mountain, the Arkenstone was sort of “depressed” and, if given some time in proper lighting, the Arkenstone would shine more brightly again.
The silmarils were said to have a great hold on the people that saw them - it explains why so many people became obsessed with the jewels (Feanor, Morgoth, Thingol, the dwarves of Nogrod, etc.). The Arkenstone does seem to have something of the same effect, if not a weaker version of it. Thror, Thorin, and even Bilbo, seem drawn to the jewel.
It’s also pointed out that the silmarils could not be cut or damaged by any force on earth, so the claim that the dwarves carved the Arkenstone into a faceted jewel is a problem. Fans supporting the silmaril theory argue that this could just be a historical inaccuracy. Perhaps the stone was found already carved, but future generations assumed that the carving must have been done by the dwarves that found it.
Finally, an argument against the idea that the Arkenstone is a silmaril is Mandos’ prophecy regarding the silmarils. He states after the War of Wrath that the three silmarils will never be found (but what about just one?), and that “the fates of Arda, earth sea and air, lay locked within them.” The common interpretation of this is that the silmarils are destined to stay separated in the three elements until the Dagor Dagorath.
But Gwaihir the Windlord (avatar, not the actual character) offers a fascinating alternate interpretation in this article. They argue that the prophecy actually means that each silmaril will play an important part in Arda’s fate. The silmaril in the air (worn still by Earendil as he sails the skies) played a huge part in the War of Wrath, allowing Earendil to fight off the winged dragons and turning the tide of the battle. If the Arkenstone is a silmaril, then it played a large part in the Third Age, motivating the defeat of Smaug, the creation of a new alliance between elves and dwarves in the north, and seeing to the discovery of the One Ring. The only silmaril that hasn’t played its part, as far as we know, is the one that was thrown into the sea.
These are the main arguments in the Arkenstone/silmaril debate. At the end of the day, there’s no real proof (especially anything said by Tolkien) to suggest that the Arkenstone is a silmaril. But it’s an interesting theory, and if you agree with the theory it adds a new level of significance to many of the events in The Hobbit.
SOURCES: The Silmarillion, The Hobbit, “Was the Arkenstone of Thrain really Maedhros’ lost Silmaril?”