Based on the idea of emergent spacetime, we consider the possibility that the material underlying our spacetime is modelled by a fluid. We are particularly interested in possible connections between the geometrical properties of the emergent spacetime and the properties of the underlying fluid. We find some partial results that support this possibility. By using the Kerr spacetime as an example, we construct from the Riemann curvature tensor a vector field, which behaves just like the speculated fluid flow.Comment: A mistake corrected, results improved, paper fully revised to account for the change. 12 page
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