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The electrostatic view on M-theory LLM geometries

We describe the geometry of the R x SO(3) x SO(6) x U(1) invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS_4 x S^7 and AdS_7 x S^4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvature.