Asymptotic Conformal Yano--Killing Tensors for Schwarzschild Metric

TL;DR

This paper analyzes the asymptotic conformal Yano--Killing tensor in Schwarzschild spacetime, showing that certain asymptotic conditions eliminate supertranslation ambiguities and define 14 gravitational charges.

Contribution

It provides a detailed analysis of the asymptotic conformal Yano--Killing tensor for Schwarzschild metric and clarifies conditions under which supertranslations vanish and gravitational charges are well-defined.

Findings

Schwarzschild metric satisfies stronger asymptotic conditions.

Supertranslation ambiguities disappear under these conditions.

14 gravitational charges are well-defined on the Schwarzschild background.

Abstract

The asymptotic conformal Yano--Killing tensor proposed in J. Jezierski, On the relation between metric and spin-2 formulation of linearized Einstein theory [GRG, in print (1994)] is analyzed for Schwarzschild metric and tensor equations defining this object are given. The result shows that the Schwarzschild metric (and other metrics which are asymptotically ``Schwarzschildean'' up to O(1/r^2) at spatial infinity) is among the metrics fullfilling stronger asymptotic conditions and supertranslations ambiguities disappear. It is also clear from the result that 14 asymptotic gravitational charges are well defined on the ``Schwarzschildean'' background.