The project's primary facility appears to have been Aquatic Base, a high-tech laboratory complex located beneath the waters of Kingdom Valley. Its duration is unspecified, but the game shows that the project ended in disaster some ten years prior to the main events of the storyline.
The public face of the Solaris Project held it to be an energy research program. However, in actuality its scope was far more ambitious: to achieve nothing less than control of time itself, through study and manipulation of a super-dimensional phenomenon called the Flame of Hope - otherwise known as Solaris, worshiped as a sun god by the people of Soleanna.
The Duke of Soleanna is presumed to have been the driving force behind the Solaris Project (although Lord Regis states that he himself worked with the Duke on the program). His exact motivations for conducting the dangerous research are uncertain. When shown talking about the project to his daughter Elise during a flashback at the end of Sonic '06, the Duke outlines a utopian vision of a timeline where humanity has erased its past mistakes. However, when questioned by Elise, he significantly adds "Yes, Elise. We'll both be able to see your mother once again..." - a line which casts some doubts upon the Duke's supposedly selfless humanitarianism.
Failure and aftermath
When Shadow and Silver travel into the past during Sonic '06, they observe firsthand the disaster which violently curtailed the project. A spatial meltdown causes an explosion in Aquatic Base's control room, killing most of the technicians and mortally wounding the Duke. But even more ominously, the accident caused Solaris to split into two component beings, Mephiles and Iblis. Shadow and Silver were able to seal these two entities inside the Scepter of Darkness and a young Princess Elise respectively, preventing any further damage to the facility.
The Solaris Project's destruction also resulted in the abandonment of the immense Soleannean royal palace in Kingdom Valley.
Years later, and despite the cordon of official secrecy, Doctor Ivo Robotnik (aka Doctor Eggman) was able to learn of the Solaris Project. He went on to reproduce and surpass the work of the Duke; using a Chaos Emerald, rather than the energies of Solaris, within his system, the Doctor was able to build a working time machine in his base at White Acropolis. However, Eggman would admit to a captured Elise that in order to perfect his machine, he needs the Flames of Disaster - another name for Iblis, one of the sundered halves of Solaris.
Implications and paradox
In creating Mephiles the Dark and Iblis, the Solaris Project provided the primary antagonists for Shadow and Silver's stories during Sonic '06 respectively. While Sonic's quest centers around thwarting Eggman's plans to twist the project's science towards his own nefarious goals, Shadow pursues (and is pursued by) Mephiles - a villainous and manipulative being who seems to embody Solaris' intelligence and cunning. Meanwhile, Silver and Blaze principally concern themselves with Iblis, a monstrous fire-creature which serves as a manifestation of Solaris' hunger for power.
As with all the events of Sonic the Hedgehog (2006), the Solaris Project is presumably erased from the timeline when Elise extinguishes the Flame of Hope at the very end of the game. How exactly the paradox resolves is unknown; however, it seems most likely that while the project was initiated in the revised timeline, the destruction of the Flame partway through meant that it could not continue, meaning all the events occurring during the project from that point on never happened.
↑During the cutscene when Shadow and Rouge arrive at the GUN rendezvous point in Kingdom Valley, Rouge explains "I hear a prototype energy engine failed, which caused the accident."
↑It isn't known precisely why the castle was abandoned, as the explosion witnessed by Silver and Shadow doesn't seem nearly violent enough to threaten either Aquatic Base or Kingdom Valley as a whole. It may be that cordoning off Kingdom Valley was more of a cover-up than a safety concern, to prevent the public from discovering the true nature of the Solaris Project: part time-travel experiment, part deicide.