Abstract
The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordström solution in the limit as the range parameter μ goes to zero. The additional terms in the g 00 metric coefficient are positive, as in Reissner-Nordström, in agreement with previous numerical solutions, and hence involve naked singularities.
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Vuille, C., Ipser, J. & Gallagher, J. Einstein-Proca Model, Micro Black Holes, and Naked Singularities. General Relativity and Gravitation 34, 689–696 (2002). https://doi.org/10.1023/A:1015942229041
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DOI: https://doi.org/10.1023/A:1015942229041