Conference

The first iteration of the second-order self-force calculation considered the problem in the Lorenz gauge. However, in the absence of a separable Lorenz gauge formalism for the astrophysical relevant scenario of Kerr spacetime, we are now pursuing a second-order calculation for the Teukolsky equation. In this talk I outline the numerical implementation to compute the second-order Weyl scalar. In lieu of the second-order Teukolsky source I will demonstrate the code by presenting results for the slow-time derivative of the (first-order) Weyl-scalar as this alternative calculation is structurally similar to the second-order calculation.

Precise parameter extraction from EMRI signals requires, among other things, the dissipative piece of the second-order self-force in a Kerr background. We have shown how a new form of the second-order Teukolsky equation has a well-defined source in a highly regular gauge, and how to construct gauge invariant second-order quantities using a gauge fixing method. For the current prospective second-order self-force methods in Kerr solving the second-order Teukolsky equation will be a crucial step. In this talk, I show our progress in calculating the source in the second-order Teukolsky equation for quasi-circular orbits in Schwarzschild, and discuss how the source can be made more regular at future null infinity by transforming to the Bondi-Sachs gauge.

One contribution to the second-order self-force calculations is the derivative of the first-order metric perturbation with respect to the slow inspiral time. Previous methods to compute this involve non-compact source terms which are challenging to work with. We employ the method of partial annihilators to obtain higher-order differential equations with a compact source, and solve these equations for the slowtime derivatives of the Regge-Wheeler and Zerilli master functions for circular orbits. We then use a gauge transformation to compute the slowtime derivative of the first-order Lorenz gauge metric perturbation.

Within the framework of self force theory we compute the gravitational wave flux through second-order in the mass ratio for quasi-circular compact binaries. Our results are consistent with post-Newtonian calculations in the weak field and we find they agree remarkably well with numerical relativity simulations of comparable mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary.

LISA science will require EMRI waveforms that are accurate to first-post-adiabatic order, which in turn requires the calculation of second-order self-force effects. In this talk I describe a post-adiabatic waveform-generation framework and progress toward its implementation. This lays the groundwork for talks by Durkan, Warburton, Spiers, Leathers, Upton, and others.