On Newman-Penrose constants of stationary space-times

TL;DR

This paper proves that all Newman-Penrose constants vanish in stationary space-times by analyzing the asymptotic structure and using Killing equations to relate gravitational wave components.

Contribution

It provides a general proof that Newman-Penrose constants are zero for stationary space-times, extending previous results with a new algebraic approach.

Findings

All Newman-Penrose constants vanish in stationary space-times.

The dynamical freedom reduces to the in-going gravitational wave component.

The proof uses asymptotic algebraic special conditions.

Abstract

We consider the general asymptotic expression of stationary space-time. Using Killing equation, we reduce the dynamical freedom of Einstein equation to the in-going gravitational wave $\Psi_0$. The general form of this function can be got. With the help of asymptotically algebraic special condition, we prove that all Newman-Penrose constants vanish.