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Self-force theory is the leading method of modeling extreme-mass-ratioinspirals (EMRIs), key sources for the gravitational-wave detector LISA. It iswell known that for an accurate EMRI model, second-order self-force effects arecritical, but calculations of these effects have been beset by obstacles. Inthis letter we present the first implementation of a complete scheme forsecond-order self-force computations, specialized to the case of quasicircularorbits about a Schwarzschild black hole. As a demonstration, we calculate thegravitational binding energy of these binaries.

Second-order self-force calculation of the gravitational binding energy in compact binaries