Note on the asymptotic structure of Kerr-Schild form

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.

Notes on self-dual gravity

“…In this paper, we find that the self-dual condition will not reduce the asymptotic symmetries at null infinity in four dimensions which is still the full BMS symmetry rather than a subset. The reduction of the asymptotic symmetry in [29] can be from some kind of linearization of the theory, see also [58] for relevant discussions. The self-dual gravity was known to have an infinite ladder of symmetries [59][60][61], which can be seen as the origin of recently discovered celestial w 1`8 symmetries [62].…”

Notes on self-dual gravity

“…The reduction of the asymptotic symmetry in [29] is due to the light-cone conditions. The subset BMS symmetry can be recovered from the full BMS symmetry by certain reductions in the self-dual solution space (see also [58] for relevant discussions). The self-dual gravity was known to have an infinite ladder of symmetries [59][60][61], which can be seen as the origin of recently discovered celestial w 1+∞ symmetries [62].…”

Kerr–Schild Tetrads and the Nijenhuis Tensor

“…[9]). In particular, the metric tensor in the form of Equations ( 1) and ( 2) may be treated as exact linear perturbations of the Minkowski space-time [10,11]. Some recent investigations on the Kerr-Schild form are given in Refs.…”