Parameterized and Consistency Tests of Gravity with Gravitational Waves: Current and Future

Gravitational wave observations offer unique opportunities to probe gravity in the strong and dynamical regime, which was difficult to access previously. We here review two theory-agnostic ways to carry out tests of general relativity with gravitational waves, namely (i) parameterized waveform tests and (ii) consistency tests between the inspiral and merger-ringdown portions. For each method, we explain the formalism, followed by results from existing events, and finally we discuss future prospects with upgraded detectors, including the possibility of using multi-band gravitational-wave observations with ground-based and space-borne interferometers. We show that such future observations have the potential to improve upon current bounds on theories beyond general relativity by many orders of magnitude. We conclude by listing several open questions that remain to be addressed.Comment: To appear in the proceedings of the conference 'Recent Progress in Relativistic Astrophysics', Shanghai, China, 6-8 May 2019; Fixed error on Fig. 4 axis label; Updated DECIGO noise curve; Fixed typo in equation

Regularizing Parameterized Black Hole Spacetimes with Kerr Symmetries

Parameterized 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 parameterized 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 parameterized Kerr spacetime. We propose two restricted classes of the refined parameterized 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 parameterized 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 parameterized 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.Comment: 21 pages, 8 figures; added an appendix and references; accepted for publication in PR