Integrability and action-angle variables for eccentric, spinning black-hole binaries in post-Newtonian theory

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• Dr. Leo Stein, The University of Mississippi
• Wednesday 26 January 2022, 14:00-15:00
• ONLINE - Details to be sent by email.

If you have a question about this talk, please contact Bipasha Chakraborty.

Note unusual time

Accurate gravitational waveforms are necessary for LIGO and LISA sources, and especially for the prospect of multi-band gravitational wave observations. Computing these waveforms accurately is expensive because of the complicated precession dynamics over a very large number of orbits. The most complicated scenario is an eccentric binary where both spins and the orbital plane are precessing. Current state-of-the-art waveform models rely on analytical approximations like orbit averaging and a small-eccentricity expansion. I will present work towards avoiding these approximations by exploiting integrability of the Hamiltonian dynamics of eccentric, spinning black hole binaries. Integrability lets us construct action-angle variables, which make the evolution very simple for arbitrarily long times. I will present how to construct the action integrals (involving lifting via a momentum map) and angle variables at 1.5PN. And while post-Newtonian corrections break integrability, we can recover it in a perturbative sense. I will also present explicit (perturbative) constants of motion at 2PN order, and the method that we used to find them. (Based on 2012.06586 and 2110.15351)

This talk is part of the Theoretical Physics Colloquium series.

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