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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 ageneral-relativistic geoid, restricted to stationary spacetimes, was presentedin terms of "isochronometric surfaces". In this note, we explicate how thisdefinition is just a special, highly restrictive case of our earlierformulation of the general-relativistic geoid using quasilocal frames, which isvalid for generic, non-stationary spacetimes [M. Oltean, R.J. Epp, P.L.McGrath, and R.B. Mann, Class. Quantum Grav. 33, 105001 (2016)]. Moreover, likethe isochronometric surface geoid, we show how our "geoid quasilocal frame"(GQF) can also be defined, simply and operationally, in terms of redshiftmeasurements.

Relativistic geoids and time dependence: quasilocal frames versus isochronometric surfaces