Orbital eccentricity in general relativity from catastrophe theory

Understand

While the orbital eccentricity is a key feature of the gravitational two-body problem, providing an unambiguous definition in general relativity poses significant challenges.

• Despite such foundational issue, the eccentricity of binary black holes has important implications in gravitational-wave astronomy.
• We present a novel approach to consistently define the orbital eccentricity in general relativity, grounded in the mathematical field of catastrophe theory.
• Specifically, we identify the presence of catastrophes, i.e., breakdowns of the stationary-phase approximation, in numerical relativity waveforms and exploit them to develop a robust and fully gauge-invariant estimator of the eccentricity.