Taub numbers are studied on asymptotically flat backgrounds with Killing
symmetries. When the field equations are solved for a background spacetime and
higher order functional derivatives (higher order variational derivatives of
the Hilbert Lagrangean) are solved for perturbations from the background, such
perturbed space-times admit zeroth, first, and second order Taub numbers.
Zeroth order Taub numbers are Komar constants (upto numerical factors) or
Penrose-Goldberg constants of the background. For a Killing symmetry of the
background, first order Taub numbers give the contribution of the linearized
perturbation to the associated backgound quantity, such as the perturbing mass.
Second order Taub numbers give the contribution of second order perturbations
to the background quantity. The Bondi mass is a sum of first and second order
Taubs numbers on a Minkowski background.Comment: To appear in the proceedings of the 8th Marcel Grossmann Conferenc
