A discontinuous Galerkin method for the distributionally-sourced s=0 Teukolsky equation

The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) is primarily sensitive to Extreme Mass Ratio Inspirals (EMRI) where the mass ratio between two black holes is higher than 10⁵. For the matched filtering process, we need a highly accurate template wave bank. In this talk, I will describe a Discontinuous Galerkin (DG) method for simulating waveforms from EMRI systems. We reduce the Teukolsky equation, which governs the behavior of EMRIs, to a set of coupled 1+1D wave equations and apply the DG method to it with a delta source term, acting like the secondary black hole in an EMRI system. Unlike other numerical schemes, our DG method can exactly incorporate the point particle behavior of the smaller black hole in the form of a delta function. Due to the spectral convergence properties of the scheme, our efficient method generates highly accurate waveforms in a very short time as compared to other methods. We have also introduced the hyperboloidal layers in our time domain solver that gives us access to the solution at null infinity. We verify our computation by computing Price tail power laws and scalar energy fluxes at null infinity.