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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The Lorentz group generators, which are put into the acceleration connection coefficients in the usual local treatment of an accelerating observer (see Ref. 1 and Ref. 3), will appear in Eq. (3.1) upon differentiation of the Lorentz transformation in the J matrix. Also, see Ref. 12 and 13 for flat space‐time results.
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© 1983 American Institute of Physics.
1983
American Institute of Physics
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