Towards exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the Teukolsky equation with singular source terms

Laser Interferometer Space Antenna (LISA), a future space-borne gravitational wave detector, is primarily sensitive to Extreme Mass Ratio Inspirals (EMRIs), which are black hole mergers with a mass ratio greater than 100,000. We require an extremely precise template wave bank for the matched filtering procedure. In this talk, I will discuss about a Discontinuous Galerkin (DG) technique for gravitational wave simulations of EMRI systems. The Teukolsky equation, which governs the behavior of EMRIs, is first reduced to a set of coupled 1+1D wave equations with a delta source term that functions as the secondary black hole in an EMRI system. Our DG approach, in contrast to previous numerical schemes, can precisely incorporate the smaller black hole's point particle behavior in the form of a delta function. Compared to previous methods, our efficient method produces very accurate waveform due to the scheme's spectral (super)convergence property and exact treatment of the Dirac delta function that models the smaller black hole. Our time domain solver now includes hyperboloidal layers, which allow us to retrieve the solution at null infinity. We verify our computation by calculating Kerr and Schwarzschild energy fluxes from circular orbits at null infinity and Price tail power laws.