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Gravitational Multipoles in General Stationary Spacetimes

by Daniel R. Mayerson

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Submission summary

Authors (as registered SciPost users): Daniel Mayerson
Submission information
Preprint Link:  (pdf)
Date submitted: 2022-12-19 14:21
Submitted by: Mayerson, Daniel
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
Approach: Theoretical


The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that these formalisms generalize to non-vacuum stationary solutions, except in a few special cases. This short letter fills this gap and shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes, for metrics that are sufficiently smooth at infinity and under a mild topological condition on the spacetime (which is automatically satisfied for black holes). The proof of equivalence between the Geroch-Hansen and Thorne formalisms, hitherto only established for stationary vacuum spacetimes, is similarly generalized to arbitrary stationary spacetimes.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2023-2-6 (Invited Report)


1- Well written
2- Interesting Idea


1 - Uniqueness is not clear
2 - No example is given


There are a few queries, after which I will be happy to reconsider for publication.

Requested changes

Please see the attached file.


  • validity: good
  • significance: good
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2023-1-20 (Invited Report)


This is a nice and well written paper, including some improvements of the literature on gravitational multipole moments, extending the Geroch-Hansen definition to stationary non-vacuum spacetimes, and its equivalence with Thorne's definition. I do recommend its publication in SciPost. However, I have several questions and comments, addressing which hopefully helps improving the paper before its publication.


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

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Anonymous on 2023-01-22  [id 3258]


There was an error in the equation at the end of the referee report. This invalidates the last comment of the referee report and therefor it can be discarded.

The attached file is an updated report.