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Memory in de Sitter space and BMS-like supertranslations

Yuta Hamada, Min-Seok Seo, Gary Shiu

TL;DR

The paper investigates how gravitational memory in de Sitter spacetime can be understood as a diffeomorphism effect, extending the flat-space memory–BMS correspondence to an expanding universe. It identifies a BMS-like supertranslation in the static patch and constructs a memory-diffeomorphism link in both the static and Poincaré/cosmological patches, showing memory is encoded by a function f via C_{zz}=2 D_z^2 f and f_fin determined by energy flux. The approach relies on a large-r, H^{-1} expansion and avoids small-source-detector separation assumptions, potentially generalizing to other FLRW spacetimes and to ordinary memory from massive messengers. These results illuminate the infrared structure of gravity in curved backgrounds and hint at how black hole hair might be described in expanding universes.

Abstract

It is well known that the memory effect in flat spacetime is parametrized by the BMS supertranslation. We investigate the relation between the memory effect and diffeomorphism in de Sitter spacetime. We find that gravitational memory is parametrized by a BMS-like supertranslation in the static patch of de Sitter spacetime. We also show a diffeomorphism that corresponds to gravitational memory in the Poincare/cosmological patch. Our method does not need to assume the separation between the source and the detector to be small compared with the Hubble radius, and can potentially be applicable to other FLRW universes, as well as "ordinary memory" mediated by massive messenger particles.

Memory in de Sitter space and BMS-like supertranslations

TL;DR

The paper investigates how gravitational memory in de Sitter spacetime can be understood as a diffeomorphism effect, extending the flat-space memory–BMS correspondence to an expanding universe. It identifies a BMS-like supertranslation in the static patch and constructs a memory-diffeomorphism link in both the static and Poincaré/cosmological patches, showing memory is encoded by a function f via C_{zz}=2 D_z^2 f and f_fin determined by energy flux. The approach relies on a large-r, H^{-1} expansion and avoids small-source-detector separation assumptions, potentially generalizing to other FLRW spacetimes and to ordinary memory from massive messengers. These results illuminate the infrared structure of gravity in curved backgrounds and hint at how black hole hair might be described in expanding universes.

Abstract

It is well known that the memory effect in flat spacetime is parametrized by the BMS supertranslation. We investigate the relation between the memory effect and diffeomorphism in de Sitter spacetime. We find that gravitational memory is parametrized by a BMS-like supertranslation in the static patch of de Sitter spacetime. We also show a diffeomorphism that corresponds to gravitational memory in the Poincare/cosmological patch. Our method does not need to assume the separation between the source and the detector to be small compared with the Hubble radius, and can potentially be applicable to other FLRW universes, as well as "ordinary memory" mediated by massive messenger particles.

Paper Structure

This paper contains 10 sections, 47 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The memory effect
  3. BMS transformation
  4. Memory in Minkowski spacetime
  5. Memory in de Sitter spacetime
  6. Static patch
  7. Poincare patch
  8. Summary
  9. Solution in the static patch of de Sitter
  10. Patches in de Sitter space

Figures (1)

  • Figure 1: A schematic picture of the memory effect. The red line corresponds to the worldline of the detector. The blue region represents the emission of a pulse, $T_{uu}\neq0$. Except for the blue region, the energy momentum tensor is zero. The memory effect is a change of the distance of the detector before and after the emission of a pulse.