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.

To every axi-symmetric isolated horizon we associate two sets of numbers, M< sub> n and
J< sub> 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.