Abstract

This paper discusses the physical effect of gravity on space, a rather treacherous topic that has not gained much attention in the literature, unlike the effect of gravity on time which has been clearly established from the beginning as a consequence of the Equivalence Principle and also experimentally tested. The difficulties encountered in analysing the effect of gravity on space can be represented by the need to compare vectors associated with different spatial points in a curved manifold, where the parallel-transport of vectors depends on the chosen path. This same problem can also be seen from another perspective: the effect of gravity on space is embodied in the components of the metric tensor, which however are not uniquely determined as a consequence of the degrees of freedom due to the Bianchi identities. We here show that, however, there are circumstances under which these difficulties can be overcome, resulting in a clear representation of the effect of gravity on space. This effect is perfectly dual to the corresponding effect on time: while gravity slows down time, it expands space. This can clarify topics like the effects of gravity at the centre of a spherically symmetric system, where the literature does not provide clear answers. A final confirmation of the gravitational expansion of space is provided by the Equivalence Principle. The conclusions help fill a conceptual gap that has so far prevented gravitational effects on time and space from being viewed on an equal footing.