Gravitational memory in higher dimensions

Abstract

It is shown that there is a universal gravitational memory effect measurable by inertial detectors in even spacetime dimensions d ≥ 4. The effect falls off at large radius r as r 3−d .Moreover this memory effect sits at one corner of an infrared triangle with the other two corners occupied by Weinberg's soft graviton theorem and infinite-dimensional asymptotic symmetries.

Classical proof of the classical soft graviton theorem in D>4

“…In this appendix we shall verify the general form (3.6) of the stress tensor associated with massless fields by explicitly constructing the stress tensor of massless scalar, vector and tensor fields. The asymptotic form of various massless fields that we shall use for this computation can be found in [37,38], but we also review their derivation. To simplify notation, we shall drop the subscript R from T Rµν and drop the primes from the coordinate labels used in (3.6).…”

“…We shall use Lorentz gauge. In the Bondi coordinates, the equations of motion A µ = 0 take the form [37,38]:…”

“…which induces a transformation We can now write down the h µν = 0 equations in the Bondi coordinate system, and substitute (B.32) into these equations to determinef µν 's in terms of f µν 's as in the case of scalar fields and gauge fields. Explicit form of these equations can be found in [37,38]. For the sake of…”

Electromagnetic and color memory in even dimensions

“…(see (B.24)), which would be leading with respect to those displayed in (2.14), for suitable values of k, but which do not contribute to the memory effect because they integrate to zero. The null memory formula then reads 16) where this result is exact for the solution considered, while for more general solutions of the wave equation in the form (B.23) it would provide the leading-order contribution.…”

“…In Section 3 we discuss various types of memories for Maxwell's theory in even-dimensional spacetimes. Upon employing a recursive gauge-fixing procedure, analogous to the one adopted in [16] in the gravitational setup, we clarify the interpretation of both ordinary and null memory in any even D as a residual gauge transformation acting at order r 4−D . We generalise this procedure to the non-Abelian case in Section 4, where we obtain similar results and interpretation for linear and non-linear memory effects concerning matter in interaction with Yang-Mills radiation.…”