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Gravitational Multipoles in General Stationary Spacetimes
by Daniel R. Mayerson
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|Authors (as registered SciPost users):||Daniel Mayerson|
|Preprint Link:||https://arxiv.org/abs/2210.05687v1 (pdf)|
|Date submitted:||2022-12-19 14:21|
|Submitted by:||Mayerson, Daniel|
|Submitted to:||SciPost Physics|
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.
Submission & Refereeing History
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- Report 2 submitted on 2023-02-06 05:44 by Anonymous
- Report 1 submitted on 2023-01-20 14:22 by Anonymous
Reports on this Submission
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.
Please see the attached file.
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.