Schwarzschild-Bach black holes

Šimon Knoška The spherically symmetric spacetimes represent one of the most important classes of solutions in general relativity. Therefore, it is very natural to study them also in the context of modified theories of gravity. We directly continue in the previous works in quadratic gravity, where the generalised solutions with the constant Ricci scalar were found in the form of power series expansion in the conformal coordinates. In this work, we have found an alternative expression of this solution in the Robinson-Trautman-like coordinates analogously in the form of power series expansion around the horizon. Al- though the prescribed recurrent power series solution is more complicated than that in the conformal-to-Kundt coordinates, it posses numerous advantages. Namely, the trans- formation to the Schwarzschild-like coordinates is considerable simple and the physical interpretation of the coordinates is more evident. These properties are demonstrated in the preliminary investigation of the geodesic motion of the test particles near the black hole with analysis of the effect of the so-called Bach parameter. In particular, we have observed that the Bach parameter together with the positive cosmological constant Λ > 0 has a significant impact on the global structure of the spacetime