Early radiative properties of the developments of time symmetric, conformally flat initial data

TL;DR

This paper calculates the early radiative properties of time symmetric, conformally flat initial data in general relativity, revealing how Newman-Penrose constants relate to incoming radiation and comparing different initial data sets.

Contribution

It introduces an expansion for the Bondi mass using conformal geodesics and links Newman-Penrose constants to incoming radiation in spacetime.

Findings

Bondi mass matches ADM mass where null infinity touches spatial infinity

Second term in expansion relates to Newman-Penrose constants

Newman-Penrose constants may measure incoming radiation

Abstract

Using a representation of spatial infinity based in the properties of conformal geodesics, the first terms of an expansion for the Bondi mass for the development of time symmetric, conformally flat initial data are calculated. As it is to be expected, the Bondi mass agrees with the ADM at the sets where null infinity ``touches'' spatial infinity. The second term in the expansion is proportional to the sum of the squared norms of the Newman-Penrose constants of the spacetime. In base of this result it is argued that these constants may provide a measure of the incoming radiation contained in the spacetime. This is illustrated by means of the Misner and Brill-Lindquist data sets.