Radiation Reaction Problem Research Articles

Gravitational radiation reaction in the Newtonian limit

The asymptotic approximation scheme based on the theory of the Newtonian limit developed in the preceding paper is applied to the gravitational radiation-reaction problem. All divergences encountered in previous approaches disappear: For any $\ensuremath{\epsilon}$ the asymptotic approximation is finite to all orders we have calculated, even beyond radiation-reaction order. This is because the divergent terms in previous work were misordered, and make finite contributions to coefficients of lower-order terms in the asymptotic expansion. The logarithmic divergences, in particular, turn up as an ${\ensuremath{\epsilon}}^{10}$ $\mathrm{ln}\ensuremath{\epsilon}$ term in the asymptotic expansion (i.e., between 2.5 and 3 post-Newtonian order) which shows that the relativistic sequence is not ${C}^{\ensuremath{\infty}}$ at $\ensuremath{\epsilon}=0$. This does not, however, affect the asymptotic convergence of the approximation. The radiation-reaction terms are used to calculate the period shortening of a nearly-Newtonian binary system directly from the equations of motion, avoiding the well-known difficulties associated with energy in general relativity. It is proved that the prediction derived from the standard quadrupole formula applies in the Newtonian limit. It is also shown that random data for the initial gravitational wave field do not affect the calculation of radiation reaction, even if their amplitude is of first post-Newtonian order.

The Problem of Radiation Reaction in Classical Electrodynamics

Abstract A new covariant theory of the classical radiating electron is compared with other radiation reaction theories: On the one hand, the new theory can be deduced from Caldirola's finite-dif-ferences theory by suitable approximations; on the other hand, the Lorentz-Dirac theory and the theory of Mo and Papas are shown to be approximative forms of the new theory. The latter is free from the difficulties of the other theories: there are no undetermined internal oscillations, no runaway solutions and pre-acceleration effects, and radiation reaction exists in the case of one-dimensional motion. The general energy-momentum balance is studied, and the implications of the existence of radiation reaction in a static constant force field are discussed with regard to the principle of equivalence.

Radiation damping as an initial value problem

Using a simple, exactly soluble model for the interaction of one particle and a scalar field Φ, we discuss the problem of radiation reaction in terms of the initial value solution. We show that if the Cauchy data of the field fall off at spatial infinity in such a way that the field has finite energy, the particle motion is damped for t → ∞. Further, we point out that no solutions with finite field energy exist for the boundary conditions Φ out = 0 and Φ in + Φ out = 0. For Φ in = 0, nontrivial solutions exist only if it is assumed that the system has been open in the past of some initial hypersurface.

Solution of radiation-reaction problem for the uniform magnetic field

An approximate solution to the classical radiation reaction for the motion of a Dirac classical particle in a uniform magnetic field is presented. The approximation involves restrictions on the magnitude of the magnetic field and on the energy associated with motion transverse and parallel to the field. Within these restrictions, the solution is valid over all proper times.

Electromagnetic scattering as a radiation reaction problem

Electromagnetic scattering is treated as a dynamical problem, by equating the external torque exerted by the incident wave on the sphere to the self torque due to the radiated (scattered) wave. ForImech=0,our scattering amplitude is equal to the usualP-wave amplitude of the electromagnetic scattering on an infinitely conducting sphere. The poles of the scattering amplitude, in particular their dependence onImech, are studied. For example, a pole on the positive imaginary axis, which usually corresponds to a bound state, corresponds to a runaway solution in our case. Non-decaying resonances are also discussed.