Parameterized Non-circular Deviation from the Kerr Paradigm and Its Observational Signatures: Extreme Mass Ratio Inspirals and Lense-Thirring Effect

Recent gravitational wave observations and shadow imaging have demonstrated the astonishing consistency of the Kerr paradigm despite all the special symmetries assumed in deriving the Kerr metric. Hence, it is crucial to test the presence of these symmetries in astrophysical scenarios and constraint possible deviations from them, especially in strong field regimes. With this motivation, the present work aims to investigate the theoretical consequences and observational signatures of non-circularity in a unified theory-agnostic manner. For this purpose, we construct a general non-circular metric with a small parameterized deviation from Kerr. This metric preserves the other properties of Kerr, such as stationarity, axisymmetry, asymptotic flatness, and the equatorial reflection symmetry. Apart from the resulting mathematical simplifications, this assumption is crucial to disentangle the consequences of relaxing circularity from other properties. Then, after discussing various novel theoretical consequences, we perform a detailed analysis of extreme mass ratio inspirals and Lense-Thirring precession in the context of this newly constructed metric. Our study clearly shows the promising prospects of detecting and constraining even a slight non-circular deviation from the Kerr paradigm using the future gravitational wave observations by the Laser Interferometer Space Antenna.