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A compact object moving on a quasicircular orbit about a Schwarzschild blackhole gradually spirals inward due to the dissipative action of itsgravitational self-force. But in addition to driving the inspiral, theself-force has a conservative piece. Within a second-order self-forceformalism, I derive a second-order generalization of Detweiler's redshiftvariable, which provides a gauge-invariant measure of conservative effects onquasicircular orbits. I sketch a frequency-domain numerical scheme forcalculating this quantity. Once this scheme has been implemented, its resultsmay be used to determine high-order terms in post-Newtonian theory andparameters in effective-one-body theory.

A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime