An exact black hole spacetime with scalar field and its shadow together with quasinormal modes

We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of the them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution.