On Black Holes in Massive Gravity

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In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. I will discuss whether these singularities can be avoided if space-time is not asymptotically Minkowskian. As an illustration, I will present an exact analytic black hole solution  which evades  the above problem by a transition at large scales to self-induced de Sitter space-time. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH  metric has to be accompanied by the St\"uckelberg fields with nontrivial backgrounds to  prevent the horizons to convert into the singularities.