  Since black holes can be formed through widely varying processes, the horizon
structure is highly complicated in the dynamical phase. Nonetheless, as
numerical simulations show, the final state appears to be universal, well
described by the Kerr geometry. How are all these large and widely varying
deviations from the Kerr horizon washed out? To investigate this issue, we
introduce a well-suited notion of horizon multipole moments and equations
governing their dynamics, thereby providing a coordinate and slicing
independent framework to investigate the approach to equilibrium. In
particular, our flux formulas for multipoles can be used as analytical checks
on numerical simulations and, in turn, the simulations could be used to fathom
possible universalities in the way black holes approach their final
equilibrium.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory