A simple black-hole-ring system is proposed as a toy model for the two-body problem in general relativity .
This toy-model yields the fractional shift \Delta \Omega _ { \text { isco } } / \Omega _ { \text { isco } } = { { 29 } \over { 81 \sqrt { 2 } } } \eta in the Schwarzschild ISCO ( innermost stable circular orbit ) frequency , where \eta \equiv m / M _ { \text { ir } } \ll 1 is the dimensionless ratio between the mass of the particle and the irreducible mass of the black hole .
Our model suggests that the second-order spin-orbit interaction between the black hole and the orbiting particle ( the dragging of inertial frames ) is the main element determining the observed value of the ISCO shift .