Gravitational Memory, BMS Supertranslations and Soft Theorems (1411.5745v1)

Abstract: The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent to Weinberg's formula for soft graviton production.

• The paper derives an explicit expression for BMS supertranslations by relating radiative energy flux moments to measurable gravitational memory effects.
• The paper establishes a direct equivalence between Weinberg's soft graviton theorem and the spatial displacement observed in gravitational memory.
• The paper suggests that BMS symmetries, acting as potential black hole hair, may offer new insights into resolving the black hole information paradox.

Gravitational Memory, BMS Supertranslations, and Soft Theorems

The paper by Andrew Strominger and Alexander Zhiboedov explores the intricate relationship between gravitational memory, BMS supertranslations, and soft theorems. This work investigates the implications of a gravitational radiation pulse transiting near future null infinity and how it induces alterations in the positional and temporal coordinates of an array of detectors. The resultant changes correspond to a BMS supertranslation, providing tangible insights into the observational consequences of BMS symmetries and their inherent connection to gravitational memory.

In the paper, the authors formulate an explicit expression for the BMS supertranslation utilizing the moments of the radiative energy flux. These theoretical underpinnings reveal that the spatial displacement memory formula aligns with Weinberg’s formula for soft graviton production. This linkage signifies that the gravitational memory effect, a measurable phenomenon, encapsulates the same physics as the less observable soft graviton production, thereby providing a practical reformulation of BMS symmetry implications.

Key Findings and Implications

The paper's central hypothesis is built upon the assertion that radiation leads to transitions between distinct gravitational vacua, distinguished by BMS supertranslations. This conceptual framework is anchored by the derived expression (equation 3.7), which is crucial for computing the supertranslation transformations.

1. Gravitational Memory and BMS Symmetry: The authors effectively demonstrate how distinct vacua states induced by gravitational radiation are related through supertranslations. Notably, the spatial displacement and potential time delays observed between detector arrays are resolved through this concept, which inherently encapsulates the gravitational memory effect.
2. Soft Theorems and Gravitational Memory: Through a detailed analysis, the paper establishes that the soft graviton theorem by Weinberg translates directly into observable gravitational memory effects. This equivalence underscores the foundational role of BMS symmetry within the broader framework of quantum gravity scattering processes.
3. Black Hole Hair: The discussion extends to consider black holes, proposing that they contain an infinite degree of BMS supertranslation hair. This introduces significant consequences for black hole information puzzles, suggesting that these symmetries retain memories of their formative processes.

Experimental Considerations and Future Directions

The paper suggests promising avenues for empirical investigation. The gravitational memory effect, while challenging to measure directly due to its deviation from typical gravitational wave observation, could yield pivotal experimental insights, especially with advanced detection arrangements like those proposed by LIGO and eLISA. Exploring practical clock desynchronization and spatial displacement effects within real-world scenarios underlines the potential for significant empirical advancements.

The consideration of BMS symmetries in practical settings could further this understanding. Through meticulous experimentation, the very nature of gravitational vacua transitions and their influence on spacetime might be deciphered. The investigation highlights the utility of gravitational memory as a probe for asymptotic symmetries, extending from general relativity into broader quantum physical contexts.

Conclusion

In essence, Strominger and Zhiboedov's paper contributes a profound understanding of gravitational memory through the lens of BMS supertranslations and their relationship to soft theorems. The reconciliation of gravitational interactions and quantum field theoretical constructs offers a compelling perspective that could illuminate the dynamics of spacetime, symmetries, and perhaps, aspects of the elusive quantum gravity. As new developments arise in detector technologies and observational capacities, validating and expanding on these theoretical revelations seems inevitable, promising exciting possibilities in understanding the universe's fundamental fabric.