An ansatz for spacetimes of zero gravitational mass : global monopoles and textures

We propose a geometric ansatz, a restriction on Euclidean / Minkowski distance in the embedding space being propotional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i u^k = 0, u_i u^i = 1$). It turns out that these spacetimes can represent global monopoles and textures. Thus the ansatz is a prescription to generate zero mass spacetimes that could describe topological defects, global monopoles and textures.

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