Solving Einstein's Equations for Binary Black Hole Spacetimes

General Relativity Theory II
The spacetime metric ψ ab is determined by Einstein’s equation:
R ab − 1 2 Rψ ab = 8πT ab ,
where R ab is the Ricci curvature tensor associated with ψ ab ,
R = ψ ab R ab is the scalar curvature, and T ab is the stress-energy
tensor of the matter present in spacetime.
For “vacuum” spacetimes (like binary black hole systems) T ab = 0,
so Einstein’s equations can be reduced to R ab = 0.
Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 5 / 32