Spherically Symmetric Static States of Wave Dark Matter

In this paper, we present two observations about static spherically symmetric solutions of the Einstein-Klein-Gordon equations. The first is a comment extending the well-known result of the existence of static states (i.e. standing wave solutions) of the Einstein-Klein-Gordon equations. The second more important observation shows that, in the low field limit, the mass profiles of these static states lie along hyperbolas of constant $Υ$, the fundamental constant of the Einstein-Klein-Gordon equations.

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