The Power of the Stars is an immense power that appeared in Sonic Rush Adventure. While little is known about this power, it has been explained by Eggman Nega that it is the force that separates and sustains the existence of parallel dimensions, such as Sonic's dimension and the Sol Dimension.
While the upper limit of the Power of the Stars is unknown, it is known that it far surpasses even the combined power of the Chaos Emeralds and Sol Emeralds, and that just a fraction of it is enough to completely annihilate Blaze's kingdom. It has a connection with the Jeweled Scepter as the Jeweled Scepter is the key to tapping the Power of the Stars, which can only be done in some ancient ruins deep beneath Southern Island. It is said that it has the power to destroy both of the realms. It can also, if the user wishes this, can merge the two realms together and the user of the power reigns as king of that realm.
Considering the Power of the Stars facilitate the existence of different dimensions, it can be presumed that it has existed since the creation of parallel dimensions. In the Sol Dimension's ancient past, an unknown civilization learned of the existence of the Power of the Stars and learned how to unlock it and harness its power with the Jeweled Scepter. Over time, the knowledge about the Power of the Stars eventually faded into legends.
The Power of the Stars is the main target of Doctor Eggman and Eggman Nega in Sonic Rush Adventure. Their master plan in the game was to harness the Power of the Stars and use it to create Eggmanland upon both Sonic's dimension and the Sol Dimension. To harness this power however, they needed the key to unlocking it; the Jeweled Scepter. They therefore created Captain Whisker and his pirate crew to seek out the Jeweled Scepter, while they sought for the place to unlock the Power of the Stars.
Despite the interference by Sonic the Hedgehog, Blaze the Cat, Miles "Tails" Prower and Marine the Raccoon, the two doctors managed to get a hold of the Jeweled Scepter and traveled to beneath Southern Island to unlock the Power of the Stars. Once there, the doctors' Egg Wizard managed to unleash the Power of the Stars and gained immeasurable power. The doctors then prepared to use it to kill Sonic and Blaze and bring the worlds to their knees, but were defeated by the combined efforts of Super Sonic, Burning Blaze and Marine, thus ending their use of the Power of the Stars. The Jeweled Scepter itself was afterwards taken into the custody of Blaze and her guards to keep anyone from abusing the scepter or the Power of the Stars again.