There is no scientific term or concept called "aestherosphere."

It's possible you're thinking of the "asthenosphere". The asthenosphere is a part of the Earth's upper mantle located below the lithosphere. It's a zone of partially molten rock that behaves like a viscous fluid over long periods, allowing tectonic plates to move on its surface.

Let me know if you had something else in mind, and I'll do my best to help!