General Coordinatisations of the Flat Space—Time of Constant Proper-acceleration

Abstract

We examine space-times which are described by a metric of the form ds² = V²(X)dT² - U² (X)dX² - dY² - dZ² in which V =V (X) and U = U(X) are continuous functions of X only and which admit diffeomorphisms into Minkowski space-time. It is shown that such space-times are associated with rigidly accelerating frames of reference by appeal to the notion of a fundamental observer. The condition for the existence of the diffeomorphism is derived from first principles and some special cases of coordinates are discussed.