New Classification of Geometries for Gravitational Waves Unveiled

Researchers Hjalte Frellesvig, Roger Morales, and Matthias Wilhelm have presented a new classification of geometries relevant to gravitational waves in their paper titled "Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov". This work, submitted to arXiv on May 27, 2024, and revised on September 2, 2024, focuses on the loop-by-loop Baikov representation to analyze Feynman integrals that contribute to the dynamics of black-hole systems within the framework of general relativity.

The authors classify geometries appearing up to three loops, corresponding to the fourth post-Minkowskian order, for all diagrams that are significant to both conservative and dissipative dynamics. Their findings align with existing literature, confirming established results in the field.

A notable aspect of their research is the examination of the non-planar top topology at four loops, which presents complex integration challenges. The authors found that this topology has an algebraic leading singularity, indicating that its behavior is influenced by non-trivial geometries through its subsectors. This classification could have implications for future studies and applications in gravitational wave research, particularly in understanding the dynamics of black-hole interactions.

The full paper can be accessed via arXiv under the identifier arXiv:2405.17255.