Abstract A rigorous non-existence proof for runaway solutions in the finite-size model of the electron is given. Since a consistent point limit, such as the Lorentz-Dirac equation claims to be, should not exhibit features which are completely missing in the more general theory of finite extension, it is proposed that the point-like approximation of the finite-size theory be the integrodifferential formulation of the Lorentz-Dirac theory. This point of view is supported by a new discussion of the hyperbolic motion in the latter theory.
The equation of motion of a high speed test particle in the field of a spherical mass is discussed for a parametric range of gravitational theories, including general relativity. It is shown how in principle such hyperbolic orbits may discriminate between these theories.
Abstract Within the framework of the finite-size model of the electron recently dovelopped the case of hyperbolic motion is studied rigorously by means of an exact solution. The energy-momentum balance is discussed as well as the critical phenomena arising if the external field strength comes into the range of order of the maximal self-field strength of the particle. It is found that the commonly accepted Lorentz-Dirac-Rohrlich theory is only a good approximation for small values of the external field strength.
Electric field of a point charge in truncated hyperbolic motion
