Last week I gave a talk at the 24th Capra Meeting on Radiation Reaction in General Relativity.

You can watch the talk here and view the slides here.

The talk, “Calculating the second-order self-force for a Teukolsky formalism” was on progress we have made on pursuing a second-order calculation for the Teukolsky equation.

We are now attaining promising results (reference second-order flux paper) through the current implementation of the second-order calculation in Lorenz gauge formulation.  The work of Niels Warburton, Adam Pound, Barry Wardell, Jeremy Miller and Leanne Durkan has yielded results for the Gravitational wave flux for compact binaries through second-order in the mass-ratio.  This is the culmination of nearly a decade of work but this was for the simplest scenario: a circular orbit in Schwarzschild spacetime. 

The original quartet of collaborators (Niels Warburton, Adam Pound, Barry Wardell, Jeremy Miller) has now grown to pursue multiple pathways to, hopefully, the physically relevant scenario of a generic orbit in Kerr spacetime.

One such route is a second-order calculation through a Teukolsky formalism.  For now, this it remains the case that we are considering a quasi-circular orbit in Schwarzschild spacetime, albeit in a new Teukolsky formalism. 

In this talk I focus on how to implement this calculation once you have all the necessary components: primarily a second-order Teukolsky source, the relevant slow-time derivatives from the Lorenz gauge metric perturbation and the transformation to the highly regular gauge ect.  Once you have all the necessary pieces, what would a calculation of this second-order field look like?