Measurement of Distance in General Relativity

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Abstract
An instrinsic geometrical definition of distance is presented in terms of the geodesic deviation of null rays. This definition is applied to the Schwarzschild solution and the homogeneous and isotropic cosmological solutions of the Einstein field equations. In the former case the distance is proportional to the radial coordinate of the standard metric and in the latter case it yields the usual cosmological distance. However, since the geodesic deviation is a scalar, the results are independent of the particular metric used. The relationship of this definition to observation is discussed and it is concluded that it agrees with the astronomical definition of luminosity distance.

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