Spherically Symmetric Solutions of a Chiral Self-Gravitating Model in $$\boldsymbol{f(R,\square R)}$$ Gravity

We construct a chiral self-gravitating model corresponding to modified $$f(R,\square R)$$ gravity following by application of the Lagrange multipliers method and a conformal transformation to obtain the model in the Einstein frame. Killing symmetries of the target space are found. Using a special case of a scaling transformation, we find examples of exact solutions with zero and constant potentials. A linear dependence between the fields leads to new solutions for the model.

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