Numerical Relativity for Inspiraling Binaries in Co-Rotating Coordinates: Test Bed for Lapse and Shift Equations

Gravitational-wave data analysis requires a detailed understanding of the highly relativistic, late stages of inspiral of neutron-star and black-hole binaries. A promising method to compute the late inspiral and its emitted waves is numerical relativity in co-rotating coordinates. The coordinates must be kept co-rotating via an appropriate choice of numerical relativity's lapse and shift functions. This article proposes a model problem for testing the ability of various lapse and shift prescriptions to keep the coordinates co-rotating.