Cauchy-Characteristic Matching in SpECTRE

The goal of numerical relativity is to extract waveforms at future null infinity so that they can be used in LIGO. A characteristic evolution of Einstein’s equations is well suited to do this because the equations are evolved on null hypersurfaces. However, these equations are ill-suited near the black holes (BHs) because the null hypersurfaces form caustics. So near the horizons we evolve Einstein's equations as a Cauchy initial value problem. The combination of using a Cauchy evolution near the BHs and a characteristic evolution in the wave-zone is known as Cauchy-Characteristic Evolution (CCE). This procedure is still subject to error because of the imperfect outer boundary conditions for the Cauchy evolution which are imposed at a finite radius. Cauchy-Characteristic Matching (CCM) solves this problem by imposing exact outer boundary conditions at null infinity for the characteristic evolution and hence for the Cauchy evolution by the matching conditions imposed at the finite outer boundary. I will present results of CCM simulations done with the SpECTRE code and compare them to simulations of CCE.