Can the essence of God be divided and not be one cohesive mass, and is this the concept of the Trinity that Christians intend?

One must be content with what is mentioned in the Sharia regarding the names and attributes of Allah, without distortion, nullification, anthropomorphism (takyif), or resemblance (tamthil). Among the meanings of Allah’s name “As-Samad” is that He is indivisible, undividable, unpartitionable, and inseparable. His essence does not accept division or partitioning, because He is not hollow, as the Salaf mentioned. As-Samad is He upon whom division and separation are impossible in any way whatsoever. It denotes collection and strength and is used for the Master, the Sought One, whom people approach for their needs.