The interactions of charged, spinning, magnetized masses (Q2752497)

The author of this interesting paper deals with the Einstein-Maxwell equations for empty space, assuming that all sources are represented by singularities: NEWLINE\[NEWLINER_k^i=2F^{ia}F_{ka}-(1/2)\delta_k^iF^{ab}F_{ab}, \quad F_{ik}=A_{i,k}-A_{k,i}, \quad F_{;k}^{ik}=0,NEWLINE\]NEWLINE where \(R_k^i\) is the Ricci tensor, \(F_{ik}\) the electromagnetic field tensor, \(A_i\) the vector potential. \(A_{i,k}\) denotes partial differentiation and \(A_{i;k}\) covariant differentiation. Space-time is stationary and axially symmetric with metric NEWLINE\[NEWLINEds^2=-f^{-1}e^{\nu }(dz^2+dr^2)-l d\theta ^2-2n d\theta dt+f dt^2,NEWLINE\]NEWLINE where \(f,\nu ,l,n\) are functions of \(z\) and \(r\) only. The coordinates are numbered by \(x^1=z\), \(x^2=r\), \(x^3=\theta \), \(x^4=t\), where \(\infty >z>-\infty \), \(r>0\), \(2\pi \geq \theta \geq 0\), \(\infty >t>-\infty \). An approximate axially symmetric stationary solution of the considered Einstein-Maxwell equations for a pair of charged, spinning, massive particles with a magnetic dipole moment is obtained. For general values of the particle parameters there are two singularities on the axis between the particles. One is the known stress singularity representing a force holding the particles apart. The other is a torsion singularity representing a couple maintaining the spins at the prescribed values. Among the effects demonstrated which might conceivably be experimentally tested are: a) a magnet in the presence of an electric charge needs a couple to stop it turning and b) a charged particle in the presence of an uncharged one produces a ghost charge at the position of the latter. The paper provides a physical explanation of a puzzling singularity in the Perjes-Israel-Walker exact solution.