The Memory Effect in Spacetimes of Dimension $d \geq 4$

General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

05 September 10:00 - 11:00

Robert Wald - The University of Chicago

We consider the asymptotic behavior of the metric in general relativity near null infinity in both even and odd dimensions with $d \geq 4$ under the ansatz that the metric has a suitable expansion in 1/r. In even dimensions, our ansatz includes all solutions that are smooth at scri; scri does not exist for radiating solutions in odd dimensions. We analyze the memory effect, i.e., the permanent displacement of test particles near null infinity following a burst of gravitational radiation. We show that in even dimensions, the memory effect first arises at Coulombic order—i.e., order 1/r^{d−3}—and can naturally be decomposed into “null memory” and “ordinary memory.” The total memory effect vanishes at Coulombic and slower fall-off in odd dimensions. 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. We discuss the relationship between memory and asymptotic symmetries/diffeomorphisms and and the relationship between memory and infrared divergences in quantum field theory.
Lars Andersson
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Mattias Dahl
KTH Royal Institute of Technology
Philippe G. LeFloch
Sorbonne University
Richard Schoen
University of California, Irvine


Mattias Dahl


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