Geoids in general relativity: geoid quasilocal frames

We develop, in the context of general relativity, the notion of a geoid-a surface of constant 'gravitational potential'. In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilo...

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Bibliographic Details
Published in:Classical and quantum gravity 2016-05, Vol.33 (10), p.105001-105023
Main Authors: Oltean, Marius, Epp, Richard J, McGrath, Paul L, Mann, Robert B
Format: Article
Language:English
Subjects:
Boundaries
conservtion laws
Constants
Frames
geoid
Geoids
geoids in stationary axisymmetric spacetimes
Gravitation
Quadrupoles
Quantum gravity
quasilocal frames
relativistic versus Newtonian geoids
Relativity
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Summary:We develop, in the context of general relativity, the notion of a geoid-a surface of constant 'gravitational potential'. In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilocal frame-that is, a choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume. We study the geometric properties of these geoid quasilocal frames, and construct solutions for them in some simple spacetimes. We then compare these results-focusing on the computationally tractable scenario of a non-rotating body with a quadrupole perturbation-against their counterparts in Newtonian gravity (the setting for current applications of the geoid), and we compute general-relativistic corrections to some measurable geometric quantities.
ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/33/10/105001