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, ..., 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.