Abstract
Generically, massive gravity gives a non-unique gravitational field around a star. For a special family of massive gravity theories, we show that the stellar gravitational field is unique and observationally acceptable, that is close to Einsteinian. The black hole solutions in this family of theories are also studied and shown to be peculiar. Black holes have a near-horizon throat and the curvature diverging at the horizon. We show that there exists a sub-family of these massive gravity theories with non-singular at horizon black holes.
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