Multipole Moments of Isolated Horizons

To every axi-symmetric isolated horizon we associate two sets of numbers, $M_n$ and $J_n$ with $n=0,1,2,\mathrm{.}\mathrm{.}\mathrm{.}$, representing its mass and angular momentum multipoles. They provide a diffeomorphism invariant characterization of the horizon geometry. Physically, they can be thought of as the `source multipoles’ of black holes in equilibrium. These structures have a variety of potential applications ranging from equations of motion of black holes and numerical relativity to quantum gravity.