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First Law of Binary Black Hole Scattering.
Riccardo Gonzo1, Jack Lewis2, Adam Pound2
1University of Edinburgh, Higgs Centre for Theoretical Physics, School of Physics and Astronomy, Edinburgh EH9 3FD, United Kingdom.
Physical Review Letters
|October 12, 2025
Summary
The first law of binary black hole mechanics is extended to scattering orbits, linking elapsed proper time to Detweiler redshift. This provides new insights into the gravitational two-body problem using high-energy physics methods.
Area of Science:
- * Astrophysics and Gravitational Physics
- * Classical Mechanics and High-Energy Physics
Background:
- * The first law of binary black hole mechanics unified the gravitational two-body problem.
- * Binary black hole scattering and high-energy physics offer new approaches to classical problems.
Purpose of the Study:
- * Extend the first law of binary black hole mechanics to scattering orbits.
- * Connect scattering orbit dynamics to bound-orbit physics.
Main Methods:
- * Derivations using classical S-matrix, Hamiltonian, and pseudo-Hamiltonian methods.
- * Inclusion of dissipative effects via the pseudo-Hamiltonian method.
- * Development of a "boundary to bound" map.
Main Results:
- * Successful extension of the first law to scattering orbits.
- * Incorporation of dissipative effects into the extended first law.
- * Mapping of elapsed proper time (scattering) to Detweiler redshift (bound orbits).
Conclusions:
- * The extended first law provides a unifying framework for both scattering and bound orbits.
- * The
- boundary to bound
- map reveals a connection between previously disparate observables.
- * This work offers a new invariant building block for gravitational waveform models.
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