In this section, we present the equations governing boson-star solutions, namely the Einstein equations for the geometry description and the Klein–Gordon equation to represent the (complex) scalar field. We refer to this coupled system as the Einstein–Klein–Gordon (EKG) equations.
The covariant equations describing boson stars are presented in Section 2.2, which is followed by choosing particular coordinates consistent with a 3+1 decomposition in Section 2.3. A form for the potential of the scalar field is then chosen and solutions are presented in Section 2.4.
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