Computing spacetime curvature via differential algebraic equations

The equations that govern the behavior of physical systems can often be solved numerically using a method of lines approach and differential algebraic equation (DAE) solvers. For example, such an approach can be used to solve the Einstein field equations of general relativity, and thereby simulate significant astrophysical events. In this paper, we describe some preliminary work in which two model problems in general relativity are formulated, spatially discretized, and then numerically solved as a DAE. In particular, we seek to reproduce the solution to the spherically symmetric Schwarzschild spacetime. This is an important testbed calculation in numerical relativity since the solution is the steady-state for the collision of two (or more) nonrotating black holes. Moreover, analytic late-time properties of the Schwarzschild spacetime are well known and can be used to verify the accuracy of the simulation.