How to observe a non-Kerr spacetime using gravitational waves

Area of Science:

• Astrophysics
• General Relativity
• Gravitational-Wave Astronomy

Background:

• Extreme-mass-ratio inspirals (EMRIs) are crucial for probing strong gravity.
• Distinguishing Kerr from non-Kerr spacetimes is vital for understanding black hole environments.
• Current methods struggle to definitively differentiate between these spacetime types.

Purpose of the Study:

• To develop a novel criterion for differentiating Kerr and non-Kerr spacetimes using gravitational-wave data.
• To identify unique signatures in gravitational-wave signals from EMRIs that indicate spacetime properties.

Main Methods:

• Utilizing the theory of integrable systems and phase space dynamics.
• Analyzing the disintegration of tori and formation of Birkhoff chains in perturbed systems.
• Examining the frequency ratios of Kolmogorov–Arnold–Moser (KAM) curves on surfaces of section.

Main Results:

• A characteristic property of KAM curves within Birkhoff chains is a constant ratio of frequencies.
• KAM curves not part of a Birkhoff chain do not exhibit this frequency ratio constancy.
• Temporal constancy of frequency ratios in gravitational-wave signals indicates a non-Kerr spacetime.

Conclusions:

• The proposed criterion offers a robust method for gravitational-wave data analysis.
• This technique can help identify deviations from the Kerr metric in astrophysical environments.
• Future observations of EMRIs can leverage this criterion to test fundamental physics.