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.
Highlights
Radiation is characterized by the news functions
It is worthwhile to emphasize that any solution of the news function and the initial data to the Kerr-Schild constraint will give a solution of vacuum Einstein equation
It can not lead to a mass loss formula which is not surprising in the sense that the radiation taking away the energy from the system should satisfy real condition
Summary
The retarded coordinates (u, r, z, z) is the most convenient choice of the coordinates system to work with physical fields at future null infinity where (z, z) is the complex stereographic coordinates that is related to the usual angular variables (θ, φ) by z. We map the celestial sphere at null infinity to a 2d plane. The connection between those two choices can be found, for instance, in [53,54,55,56]. Two standard equations: Gzz = Gzz = 0. Three supplementary equations: Guz = Guz = Guu = 0. When the hypersurface equations and standard equations are satisfied, the Bianchi identity. Gzz = 0 because of the boundary condition for gzz, which means that the trivial equation is satisfied automatically. Three supplementary equations are only left with only one order to solve in the asymptotic expansion
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