Gravitational self-force in a Schwarzschild background and the effective one-body formalism

We discuss various ways in which the computation of conservative gravitational self-force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the effective one-body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass numerical relativity data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focusing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian level, and we analytically compute the first logarithm entering a certain, gauge-invariant ``redshift'' GSF function (defined along the sequence of circular orbits).