Regularizing parametrized black hole spacetimes with Kerr symmetries
Kent Yagi, Samantha Lomuscio, Tristen Lowrey, Zack Carson
Abstract
Parametrized Kerr spacetimes allow us to test the nature of black holes in model-independent ways. Such spacetimes contain several arbitrary functions and, as a matter of practicality, one Taylor expands them about infinity and keeps only to finite orders in the expansion. In this paper, we focus on the parametrized spacetime preserving Killing symmetries of a Kerr spacetime and show that an unphysical divergence may appear in the metric if such a truncation is performed in the series expansion. To remedy this, we redefine the arbitrary functions so that the divergence disappears, at least for several known black hole solutions that can be mapped to the parametrized Kerr spacetime. We propose two restricted classes of the refined parametrized Kerr spacetime that only contain one or two arbitrary functions and yet can reproduce exactly all the example black hole spacetimes considered in this paper. The Petrov class of the parametrized Kerr spacetime is of type I while that for the restricted class with one arbitrary function remains type D. We also compute the ringdown frequencies and the shapes of black hole shadows for the parametrized spacetime and show how they deviate from Kerr. The refined black hole metrics with Kerr symmetries presented here are practically more useful than those proposed in previous literature.