The Asymptotic Behavior of Massless Fields and the Memory Effect
Abstract
We investigate the behavior of perturbations of in d >= 4 Minkowski spacetime (in both even and odd dimensions) near null infinity in full, nonlinear General Relativity under the assumption that the perturbations admit a suitable expansion in 1 / r . We explicitly obtain the recursion relations on the coefficients of the 1 / r expansion implied by the field equations (in Harmonic gauge) as well as the ``constraints''. We then consider the memory effect in fully nonlinear general relativity. We show that in even dimensions, the memory first arises at Coulombic order'i.e., order 1 /r d - 3 'and can naturally be decomposed into ``null memory'' and ``ordinary memory.'' In odd dimensions, the memory effect vanishes near null infinity at Coulombic order and slower fall-off. The null memory is always of ``scalar type'' with regard to its behavior on spheres, but the ordinary memory can be of any (i.e., scalar, vector, or tensor) type. Scalar memory is described by a diffeomorphism, which is an asymptotic symmetry (a supertranslation) in d = 4 and a gauge transformation for d > 4 . Vector and tensor memory cannot be described by diffeomorphisms.
This research was supported in part by NSF Grants PHY 15-05124 and PHY18-04216 to the University of Chicago.- Publication:
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APS April Meeting Abstracts
- Pub Date:
- 2019
- Bibcode:
- 2019APS..APRQ11001S