Definition of the relativistic geoid in terms of isochronometric surfaces

摘要: We present a definition of the geoid that is based on formalism general relativity without approximations; i.e. it allows for arbitrarily strong gravitational fields. For this reason, applies not only to Earth and other planets but also compact objects such as neutron stars. define level surface time-independent redshift potential. Such potential exists in any stationary spacetime. Therefore, our well defined rigidly rotating object with constant angular velocity fixed rotation axis subject external forces. Our operational because surfaces can be realized help standard clocks, which may connected by optical fibers. these are called isochronometric surfaces. deliberately base relativistic use clocks since we believe clock geodesy offers best methods probing fields highest precision future. However, point out mathematically equivalent terms an acceleration potential, viewed orthogonal plumb lines. Moreover, demonstrate reduces known Newtonian post-Newtonian notions appropriate limits. As illustration, determine observers axisymmetric static solutions Einstein's vacuum field equation, Schwarzschild metric, Erez-Rosen q-metric Kerr metric particular examples.