Related papers: The Lorentz-Dirac equation in complex space-time
The Newman-Janis algorithm is well known to provide rotating black holes solutions to Einstein's equations from static seeds, through a complexification of a radial and a time coordinates. However, an ambiguity remains for the replacement…
We extend Newton's problem of minimal resistance to the Lorentz-Minkowski space. We derive the functional energy and determine the Euler-Lagrange equation. In contrast to the Euclidean case, this equation is quasilinear elliptic, and thus,…
We look at the program of modelling a subatomic particle---one having mass, charge, and angular momentum---as an interior solution joined to a classical general-relativistic Kerr-Newman exterior spacetime. We find that the assumption of…
In a recent work we have proven the existence of degenerate solutions to the Dirac equation, corresponding to an infinite number of different electromagnetic fields, providing also some examples regarding massless particles. In the present…
When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a…
We investigate the local energy decay of solutions of the Dirac equation in the non-extreme Kerr-Newman metric. First, we write the Dirac equation as a Cauchy problem and define the Dirac operator. It is shown that the Dirac operator is…
Compact binaries consisting of neutron stars / black holes on eccentric orbit undergo a perturbed Keplerian motion. The perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…
We focus our attention, once again, on the Klein--Gordon and Dirac equations with a plane-wave field. We recall that for the first time a set of solutions of these equations was found by Volkov. The Volkov solutions are widely used in…
In the frame of the Kerr-Schild approach, we obtain a generalization of the Kerr solution to a nonstationary case corresponding to a rotating source moving with arbitrary acceleration. Similar to the Kerr solution, the solutions obtained…
Starting with the Dirac-Pauli equation for a massive neutrino in an external magnetic field, we propose a new quantum equation for a neutrino in the presence of the background matter. On this basis the quantum theory of a neutrino moving in…
LaTeX transcription (2025) of a 1989 honours thesis (University of Adelaide) on point charges in classical electrodynamics and the Lorentz-Dirac radiation-reaction equation. The thesis reviews the retarded field of an arbitrarily moving…
An energy-momentum carried by electromagnetic field produced by two point-like charged particles is calculated. Integration region considered in the evaluation of the bound and emitted quantities produced by all points of world lines up to…
A new class of exact solutions of the bound Dirac and bound Klein Gordon equations in non co propagating plane waves is found. The solutions are based on the physical principle of maintaining local gauge invariance in the Furry picture…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
Motivated by the need of elaboration of the quantum theory of the spin light of neutrino in matter ($SL\nu$), we have studied in more detail the exact solutions of the Dirac equation for neutrinos moving in the background matter. These…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
The massive Dirac equation on a Kerr-Newman background may be solved by the method of separation of variables. The radial and angular equations are coupled via an angular eigenvalue, which is determined from the Chandrasekhar-Page (CP)…
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the non-physical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in…
In his analysis of the Classical Theory of Radiating Electrons, Dirac (1938) draws attention to the characteristic instability of solutions to the third order equation of motion. He remarks that changing the sign of the self-force…