Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity

It is shown that Schwarzschild black hole and de Sitter solutions exist as exact solutions of a recently proposed relativistic covariant formulation of (power-counting) renormalizable gravity with a fluid. The formulation without a fluid is presented here too. The stability of the solutions is studied and their corresponding entropies are computed by using the covariant Wald method. The area law is shown to hold both for the Schwarzschild and for the de Sitter solutions found, confirming that, for the $\beta =1$ case, one is dealing with a minimal modification of general relativity.