New Solver Enhances Gravitational Wave Simulations for Extreme Mass Ratio Inspirals

Recent advancements in gravitational wave research have been made with the introduction of a new time-domain solver for the scalar Teukolsky equation, as detailed in the paper titled "Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms" by Manas Vishal, Scott E. Field, Katie Rink, Sigal Gottlieb, and Gaurav Khanna. This study focuses on the modeling of extreme mass ratio inspirals (EMRIs), which are significant sources of gravitational waves detectable by space-based observatories.

The authors describe a multi-domain discontinuous Galerkin method that addresses the challenges posed by the Dirac delta distribution used to represent smaller black holes in these systems. Traditional time-domain solvers often introduce systematic errors due to approximations made when handling this singularity. The new method achieves global spectral accuracy, even at the location of the Dirac delta, which is crucial for precise simulations.

Key findings from the study include:

• The method's numerical flux correctly accounts for the Dirac delta, enhancing accuracy in simulations.
• The hyperboloidal layer method is employed to connect near-field dynamics to future null infinity, facilitating the extraction of far-field waveforms.
• Various numerical experiments validate the method, including convergence tests and energy luminosities for circular orbits.

These advancements could significantly improve the accuracy of gravitational wave signal predictions, which is essential for the detection and analysis of EMRIs. The implications of this research extend to the computation of gravitational self-force effects, where high precision is required, particularly in the context of future gravitational wave observatories. The full paper can be accessed at arXiv:2307.01349.