Note on the asymptotic structure of Kerr-Schild form

TL;DR

This paper explores the asymptotic structure of Kerr-Schild solutions in general relativity, revealing a series of solutions near null infinity and identifying properties of the news function and specific wave solutions.

Contribution

It provides a detailed analysis of the asymptotic behavior of Kerr-Schild solutions and introduces a class of complex pp-wave solutions in closed form.

Findings

News function is chiral and does not lead to mass loss.

A series expansion of Kerr-Schild solutions around null infinity is developed.

A class of asymptotically flat complex pp-wave solutions is derived.

Abstract

The Kerr-Schild form provides a natural way of realizing the classical double copy that relates exact solutions in general relativity to exact solutions in gauge theory. In this paper, we examine the asymptotic structure of Kerr-Schild form. In Newman-Unti gauge, we find a generic solution space satisfying the Kerr-Schild form in series expansion around null infinity. The news function in the solution space is chiral and can not lead to a mass loss formula. A class of asymptotically flat complex pp-wave solutions in closed form is obtained from the solution space.