In the context of gravitational objects with spherical symmetry, we derive a solution to Einstein’s field equations using two methods leading to the same result. The first is based on a stress-energy tensor that takes into account both the electric field energy of the charge and the gravitational field energy of the mass. The second is based on the mass-energy equivalence and has more general validity. We show that the metric falls within the Weyl class of metrics, representing a static and axisymmetric solution to Einstein’s field equations. The metric, which has a form similar to that of Reisser-Nordström, is used for predictions in strong fields and possibly shows better agreement with observation in high z quasars.

We thoroughly examine the role of absolute and relative simultaneity in the interpretation of the Sagnac effect, using an approach that allows for determining the local speed along the light path. If the local speed of light is assumed to be c over the whole closed contour, there is no agreement with the observed result. There is agreement if the local speed is c along an open section of the contour only. Thus a rigorous and coherent interpretation of the Sagnac effect favours absolute over relative simultaneity. The implications for the Lorentz transformations and synchronization by means of the Global Positioning System are considered.

We investigate rigorously the behaviour of light propagation in the closed contour of the linear Sagnac effect. Assuming that the local light speed is c in a section of the contour, our approach makes it possible to determine the local speed in the other sections. We show that, if standard clock synchronization is adopted, the speed c turns out to be invariant in an open section of the contour only. Our result is due to the distinctive physical feature of the ‘time gap’ introduced by relative simultaneity in the closed contour.

The Sagnac effect can be demonstrated with light propagating either along a circular contour or, as done by Wang et al., back and forth along a linear contour. In the linear Sagnac effect, the emitter–receiver device is in motion relative to the contour where light propagates. In the reciprocal linear Sagnac effect (RLSE), the device is stationary and the contour is in motion. When the contour changes direction of motion, some special features of the linear Sagnac effect are not fully reciprocal to the RLSE, which foresees variations of the first order in v ⁄ c v/c in the round-trip time taken by a light signal to cover the contour. The RLSE can be tested with present technology and, if confirmed experimentally, it might have interesting technological applications. Presently, it can be important for testing light-speed invariance, simultaneity, and the relativity principle.