Geoids in general relativity: geoid quasilocal frames

摘要

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.