Introduction

This introductory chapter is mainly about the locality postulate of the standard relativity theory. The fundamental laws of microphysics have been formulated with respect to inertial observers. However, inertial observers do not in fact exist, since actual observers are accelerated. What do accelerated observers measure? Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. That is, an accelerated observer at each instant is equivalent to an otherwise identical momentarily comoving inertial observer. This hypothesis of locality, which underlies the special and general theories of relativity, is described in detail. The locality postulate fits perfectly together with Einstein’s local principle of equivalence to ensure that every observer in a gravitational field is pointwise inertial. When coupled with the hypothesis of locality, Einstein’s principle of equivalence provides a physical basis for a field theory of gravitation that is consistent with local Lorentz invariance.

RELATIVITY IN SPACETIMES WITH SHORT-DISTANCE STRUCTURE GOVERNED BY AN OBSERVER-INDEPENDENT (PLANCKIAN) LENGTH SCALE

I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of spacetimes whose short-distance structure is governed by an observer-independent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type E2-c2 p2-c4m2 + f(E, p, m; L p ) =0, at least for certain types of f.

The motion of a charged black hole in an electromagnetic field

The motion of a charged black hole in a weak, asymptotically uniform electric field is analysed by using the Hamiltonian formalism for coupled electromagnetic and gravitational perturbations of the Reissner-Nordstrom space-time. The hole is shown to accelerate with respect to a distant inertial observer according to Newton’s law. The relation of the approximate solution obtained to the exact solution of Ernst, representing the charged C-metric without nodal singularity, is then clarified.