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 r3−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.
Highlights
In this paper we resolve this puzzle
The effect falls off at large radius r as r3−d. 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
We show that the memory effect exhibits universal behavior, meaning that for any even d, it sits at a corner of a triangle that includes both the soft graviton theorem and asymptotic symmetries/conservation laws
Summary
Consider perturbations gμν = gμ(0ν) +hμν around a flat background in d = 2+2m dimensions, m ≥ 2. Gμ(0ν) denotes the higher-dimensional flat metric in retarded coordinates, ds2 = gμ(0ν)dxμdxν = −du2 − 2dudr + r2γABdzAdzB ,. Where zA, A = 1, · · · , 2m are coordinates on the asymptotic S2m. In an asymptotic analysis near null infinity we may include in Tμν all forms of radiative stress-energy including gravity waves. Where here and hereafter, DA denotes the covariant derivative with respect to the unit round metric γAB on S2m and D2 = γABDADB. The components of the harmonic gauge condition (2.3) are. The residual diffeomorphisms ξμ that preserve the harmonic gauge condition (2.3) obey ξμ = 0, or equivalently
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