Abstract
Recent results concerning globally isometric mappings for arbitrary observers in flat space-time are generalized to space-times admitting a time orientation. Critical to the method is the use of an orthonormal tetrad which, when it is defined globally, allows the construction of a global isometry which generalizes the pointwise boost on flat space-time. Connection coefficients are obtained, thereby defining acceleration covariant differentiation for both particle and tensor field equations. An application to orbiting observers in exterior Schwarzschild geometries is presented.
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