Merger Dynamics of N+N Co-planar Particles in Newton Gravitation

TL;DR

This paper models the inspiral and merger of co-planar particles with Newtonian mechanics plus GR-inspired corrections, revealing waveform features and internal structure insights similar to black hole mergers.

Contribution

It introduces a simplified Newtonian model with corrections that reproduces key features of black hole mergers and gravitational waveforms, providing a transparent physical interpretation.

Findings

Deformation of black hole analogs into banana-shapes.

Spiral structures in the merger product.

Qualitative agreement with numerical relativity waveforms.

Abstract

We model the inspiral and merger dynamics of two co-planar rings in Newtonian mechanics with GR motivated corrections and illustrate their similarity with those of black hole binary systems on the orbital plane. Our simulation reveals a banana-shape deformation of the ``black holes'' involved, and a typhoon-like spiral structure in the merger product. Using an eXact One-Body approach, we compute the full gravitational waveform of this process and qualitatively reproduce results consistent with those of numerical relativity. Our simulation offers a transparent link between the feature of gravitational waveforms and the internal structure of black holes, thus a complementary interpretation of physics behind numerical relativity.