# Relativistic geoids and time dependence: quasilocal frames versus isochronometric surfaces

## TL;DR

This paper compares two definitions of the relativistic geoid, showing that the quasilocal frame approach is more general and applicable to dynamic spacetimes, and demonstrates how to operationally define it via redshift measurements.

## Contribution

It demonstrates that the quasilocal frame formulation of the relativistic geoid extends the isochronometric surface approach to non-stationary spacetimes and provides an operational definition using redshift.

## Key findings

- Quasilocal frame approach is more general than isochronometric surfaces.
- The geoid quasilocal frame can be defined operationally via redshift measurements.
- The approach applies to dynamic, non-stationary spacetimes.

## Abstract

In a recent paper [D. Philipp, V. Perlick, D. Puetzfeld, E. Hackmann, and C. L\"ammerzahl, Phys. Rev. D 95, 104037 (2017)], a definition of a general-relativistic geoid, restricted to stationary spacetimes, was presented in terms of "isochronometric surfaces". In this note, we explicate how this definition is just a special, highly restrictive case of our earlier formulation of the general-relativistic geoid using quasilocal frames, which is valid for generic, non-stationary spacetimes [M. Oltean, R.J. Epp, P.L. McGrath, and R.B. Mann, Class. Quantum Grav. 33, 105001 (2016)]. Moreover, like the isochronometric surface geoid, we show how our "geoid quasilocal frame" (GQF) can also be defined, simply and operationally, in terms of redshift measurements.