The theory of relativity forbids the superluminal travel of ordinary matter. However, it is possible to amend the theory of relativity and to develop a theory permitting superluminal travel. The acceptability of the features needed for superluminal travel is discussed.

The geodesics and the curvature of a metric representing an isolated tachyon are investigated. It is argued that the properties are unphysical and inconsistent with observation, thus providing further evidence against the existence of tachyons.

In a previous paper a theoretical method permitting superluminal travel was suggested. A difficulty with the global conservation of energy and momentum is settled here.

Two problems have long been confused with each other: the gravitational redshift as discussed by the equivalence principle; and the Doppler shift observed by a detector which moves with constant proper acceleration away from a stationary source. We here distinguish these two problems and give for the first time a solution of the former which is ‘exact’ within the context of the equivalence principle in a sense discussed in the paper. The equivalence principle leads to transformations between flat spacetimes. These (...) are analyzed, and a generalized Lorentz transformation is proposed which covers transformations from inertial to uniformly accelerated frames of reference. (shrink)