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Gravitational Multipoles in General Stationary Spacetimes
by Daniel R. Mayerson
This Submission thread is now published as
|Authors (as registered SciPost users):||Daniel Mayerson|
|Preprint Link:||scipost_202305_00024v1 (pdf)|
|Date submitted:||2023-05-16 17:09|
|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 can be generalized to non-vacuum stationary solutions, except in a few special cases. This paper shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes for metrics that are sufficiently smooth at infinity. The key is the construction of an improved twist vector, which is well-defined under a mild topological condition on the spacetime (which is automatically satisfied for black holes). Ambiguities in the construction of this improved twist vector are discussed and fixed by imposing natural "gauge fixing" conditions, which also immediately lead to the equivalence between the Geroch-Hansen and Thorne formalisms for such arbitrary stationary spacetimes.
Published as SciPost Phys. 15, 154 (2023)
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The author now addresses comments raised in my previous report. I think the paper is now suitable for publication. However, I have additional comments that might be helpful in improving the presentation of the paper, but I leave it to the author to decide whether and how to implement these comments. I also think that new additions to the paper, including the field equations for the mass and spin potentials, and the relation to Kaluza Klein reduction are very interesting.