ar X iv : g r - qc / 0 10 51 09 v 1 2 8 M ay 2 00 1 Conserved quantities in a black hole collision

The Newman-Penrose constants of the spacetime corresponding to the development of the Brill-Lindquist initial data are calculated by making use of a particular representation of spatial infinity due to H. Friedrich. The Brill-Lindquist initial data set represents the head-on collision of two non-rotating black holes. In this case one non-zero constant is obtained. Its value is given in terms of the product of the individual masses of the black holes and the square of a distance parameter separating the two black holes. This constant retains its value all along null infinity, and therefore it provides information about the late time evolution of the collision process. In particular, it is argued that the magnitude of the constants provides information about the amount of residual radiation contained in the spacetime after the collision of the black holes. Introduction. Friedrich and Kánnár [5] have calculated an expression for the so-called Newman-Penrose[9] constants of time symmetric spacetimes in terms of the initial data on a spacelike Cauchy hypersurface. The Newman-Penrose constants are a set of 10 (5 complex) in general non-trivial conserved quantities defined as integrals of the form