Rapidly spinning binary black hole initial data

Numerical simulations of binary-black-hole spacetimes must begin with initial data that both satisfy the constraint equations of general relativity and lead to evolutions with the desired physical properties. We use the extended conformal thin sandwich equations to construct constraint-satisfying binary-black-hole initial data with i) nearly-maximal spins aligned with the orbital angular momentum and ii) low orbital eccentricities. Specifically, we construct conformally-flat data with dimensionless spins larger than 0.97 and conformally-curved data with spins larger than 0.995.