Conserved quantities in a black hole collision

TL;DR

This paper calculates Newman-Penrose constants for a black hole collision spacetime, revealing how these conserved quantities relate to the system's residual radiation and late-time evolution.

Contribution

It introduces a method to compute Newman-Penrose constants for black hole collisions using Friedrich's spatial infinity representation, linking constants to residual radiation.

Findings

One non-zero Newman-Penrose constant is found.

The constant's value depends on black hole masses and separation.

The constant remains invariant along null infinity.

Abstract

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.