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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We investigate gravitational radiation memory and its corresponding effect on
the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild
spacetime. First, in the context of linearized theory, we consider such a
Schwarzschild body which is initially at rest, then goes through a radiative
stage and finally emerges as a boosted Schwarzschild body. We show that the
proper retarded solution of the exterior Schwarzschild spacetime for this
process can be described in terms of the ingoing Kerr-Schild form of the
Schwarzschild metric for both the initial and final states. An outgoing
Kerr-Schild or time symmetric metric does not give the proper solution. The
special property of Kerr-Schild metrics that their linearized and nonlinear
forms are identical allows us to extend this result to processes in the
nonlinear regime. We then discuss how the nonlinear memory effect, and its
associated supertranslation, affect angular momentum conservation. Our approach
provides a new framework for studying nonlinear aspects of the memory effect.
