Multipole Moments of Isolated Horizons

TL;DR

This paper introduces a new set of multipole moments for axi-symmetric isolated horizons, providing a diffeomorphism invariant way to characterize black hole geometry with potential applications in various fields.

Contribution

It defines mass and angular momentum multipoles for isolated horizons, offering a novel invariant characterization of their geometry.

Findings

Defines multipole moments $M_n$ and $J_n$ for isolated horizons.

Provides a diffeomorphism invariant characterization of horizon geometry.

Potential applications in black hole dynamics, numerical relativity, and quantum gravity.

Abstract

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.