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All existing 4-coordinate systems centered on the world-line of anaccelerated observer are only locally defined like it happens for Fermicoordinates both in special and general relativity. As a consequence, it is notknown how non-inertial observers can build {\it equal-time surfaces} which a)correspond to a conventional observer-dependent definition of synchronizationof distant clocks; b) are good Cauchy surfaces for Maxwell equations. Anothertype of coordinate singularities are those connected to the relativisticrotating coordinate systems (the rotating disk).We show that the use ofHamiltonian methods based on 3+1 splittings of space-time allows to define asmany observer-dependent globally defined radar 4-coordinate systems as nicefoliations of space-time with space-like hyper-surfaces admissible according toM$\o$ller (for instance only differentially rotating relativistic coordinatesystem are allowed). All these conventional notions of an {\it instantaneous3-space} for an arbitrary observer can be empirically defined by introducinggeneralizations of Einstein ${1\over 2}$ convention for clock synchronizationin inertial frames. Each admissible 3+1 splitting corresponds to a non-rigidnon-inertial frame centered on the observer. When there is a Lagrangiandescription of an isolated relativistic system, its reformulation as aparametrized Minkowski theory allows to show that all the admissiblesynchronization conventions are {\it gauge equivalent}, as it also happens incanonical metric and tetrad gravity, where, however, the chrono-geometricalstructure of space-time is dynamically determined

GENERALIZED RADAR 4-COORDINATES AND EQUAL-TIME CAUCHY SURFACES FOR ARBITRARY ACCELERATED OBSERVERS