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Charges in the Extended BMS Algebra: Definitions and Applications

by M. Porrati

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Submission summary

As Contributors: Massimo Porrati
Arxiv Link: (pdf)
Date submitted: 2020-10-27 02:33
Submitted by: Porrati, Massimo
Submitted to: SciPost Physics Proceedings
Proceedings issue: 4th International Conference on Holography, String Theory and Discrete Approach in Hanoi
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


This is a review of selected topics from recent work on symmetry charges in asymptotically flat spacetime done by the author in collaboration with U. Kol and R. Javadinezhad. First we reinterpret the reality constraint on the boundary graviton as the gauge fixing of a new local symmetry, called dual supertranslations. This symmetry extends the BMS group and bears many similarities to the dual (magnetic) gauge symmetry of electrodynamics. We use this new gauge symmetry to propose a new description of the TAUB-NUT space that does not contain closed time-like curves. Next we summarize progress towards the definition of Lorentz and super-Lorentz charges that commute with supertranslations and with the soft graviton mode.

Current status:
Has been resubmitted

Submission & Refereeing History

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Submission 2010.12151v1 on 27 October 2020

Reports on this Submission

Anonymous Report 1 on 2020-11-24 (Invited Report)


This a review of three different results related to BMS symmetry in asymptotically flat spacetimes, two of which are published and one of which is unpublished. This review is short and clearly written.

On the first topic, it is not clear whether the dual supertranslation charges (7) others than the $\ell=0,1$ modes are non-vanishing in a suitable definition of locally asymptotically flat spacetimes. Indeed, for stationary spacetimes, except for the Taub-NUT spacetime no other solution of general relativity is known that admits topological charges whose backreaction extends to null infinity in the shear tensor. Therefore, all such charges might just be 0. It would be better to write that the extension of the BMS group to include dual supertranslations (in contrast to dual translations) is conjectural, and related to the existence of such non-trivial conjectural solutions.

On the second topic, the author should better comment on the role of complex gauge transformations on physical observables: for example let one take a worldline of an observer travelling through the Taub-NUT metric. If physics is consistent there should be no any imaginary number describing the trajectory of this observer. Following spacetime lines in the sense of geodesic completeness, it seems that it exists such observers that will describe a closed timelike curve. I do not see how the existence of a complex gauge transformation changes the physical experience of the observer. It would still be an unphysical solution.

I do not have comments on the third topic except that it refers in part to unpublished work, which I cannot therefore comment upon.

Requested changes

1. Better clarify that the dual supertranslation symmetry group is conjectural (if all charges are 0 for physical spacetimes), they are pure gauge.
2. Clarify the experience of a physical observer travelling through Taub-NUT : by which real process (s)he would not encounter closed timelike curves.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
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