Gravitational clock compass in General Relativity

We show how a suitably prepared set of clocks can be used to determine all components of the gravitational field in General Relativity. We call such an experimental setup a clock compass, in analogy to the usual gravitational compass. Particular attention is paid to the construction of the underlying reference frame. Conceptual differences between the clock compass and the standard gravitational compass, which is based on the measurement of the mutual accelerations between the constituents of a swarm of test bodies, are highlighted. Our results are of direct operational relevance for the setup of networks of clocks, for example in the context of relativistic geodesy.