Hyperboloidal method for frequency-domain self-force calculations

Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands metric of binary in powers mass ratio. The source perturbations depends on orbital configuration, calculational approach, and order perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, (iii) unbounded support. latter, particular, important emerging second-order (in ratio) calculations. Traditional frequency domain approaches employ variation parameters compute perturbation standard time slices with numerical boundary conditions supplied at finite radius series expansions asymptotic behavior. has been very successful, but calculations are tedious, not well suited to where homogeneous solutions must be computed all radii. work develops an alternative hyperboloidal foliate spacetime, compactifying coordinates simplify treatment. We implement this a multi-domain spectral solver analytic mesh refinement use scalar-field circular orbits around Schwarzschild black hole as example problem. works efficiently classes encountered distinct advantages over traditional approach. For example, our code computes extremely large radii ($r_{p}>10^5M$) or modes high spherical harmonic mode index ($\ell \ge 100$). Our results indicate that methods can play essential role