Regularizing Parameterized Black Hole Spacetimes with Kerr Symmetries (I): Metric

Parameterized Kerr spacetimes allow us to test the nature of black holes in model-independent ways. In the series of talks, we focus on the parameterized spacetime preserving Killing symmetries of a Kerr spacetime. In this first talk, we will show that an unphysical divergence may appear in the metric if arbitrary functions in the metric are expanded about infinity and truncated at a finite order. To remedy this, we propose to redefine the arbitrary functions so that the divergence disappears, at least for several known black hole solutions that can be mapped to the parameterized Kerr spacetime. We then explain the Petrov type of the refined parameterized Kerr spacetime.