More information about Rilles can be found
here
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Straight rilles follow long, linear paths and are believed to be grabens, sections of the crust that have sunk between two parallel faults. These can be readily identified when they pass through craters or mountain ranges.
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Precise formation mechanisms of rilles have yet to be determined. It is likely that different types formed by different processes. Common features shared by lunar rilles and similar structures on other bodies suggest that common causative mechanisms operate widely in the solar system. Leading theories include lava channels, collapsed lava tubes, near-surface dike intrusion, subsidence of lava-covered basin and crater floors, and tectonic extension.
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No splitting of moons is required.
Do not have time to have a look at it in detail right now, but
here is an article about the geology of the Moon