Kerr–Newman metric

The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass. It generalizes the Kerr metric by taking into account the field energy of an electromagnetic field, in addition to describing rotation. It is one of a large number of various different electrovacuum solutions, that is, of solutions to the Einstein–Maxwell equations which account for the field energy of an electromagnetic field. Such solutions do not include any electric charges other than that associated with the gravitational field, and are thus termed vacuum solutions. In this work we obtain an exact correspondence between the wave function of the Dirac equation and the spinor (twistorial) structure of the Kerr geometry. It allows us to assume that the Kerr–Newman geometry reflects the specific space-time structure of electron, and electron contains really the Kerr–Newman circular string of Compton size. The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass. It generalizes the Kerr metric by taking into account the field energy of an electromagnetic field, in addition to describing rotation. It is one of a large number of various different electrovacuum solutions, that is, of solutions to the Einstein–Maxwell equations which account for the field energy of an electromagnetic field. Such solutions do not include any electric charges other than that associated with the gravitational field, and are thus termed vacuum solutions. This solution has not been especially useful for describing non-black-hole astrophysical phenomena, because observed astronomical objects do not possess an appreciable net electric charge, and the magnetic field of stars arise through other processes. As a model of realistic black holes, it omits any description of infalling baryonic matter, light (null dusts) or dark matter, and thus provides at best an incomplete description of stellar mass black holes and active galactic nuclei. The solution is of theoretical and mathematical interest as it does provide a fairly simple cornerstone for further exploration. The Kerr–Newman solution is a special case of more general exact solutions of the Einstein–Maxwell equations with non-zero cosmological constant. In Dec 1963 Kerr and Schild found the Kerr-Schild metrics that gave all Einstein spaces that are exact linear perturbations of Minkowski space. In early 1964 Roy Kerr looked for all Einstein-Maxwell spaces with this same property. By Feb 1964 the special case where the Kerr-Schild spaces were charged (this includes the Kerr-Newman solution) was known but the general case where the special directions were not geodesics of the underlying Minkowski space proved very difficult. The problem was given to George Debney to try to solve but was given up by March 1964. About this time Ezra T. Newman found the solution for charged Kerr by guesswork.In 1965, Ezra 'Ted' Newman found the axisymmetric solution of Einstein's field equation for a black hole which is both rotating and electrically charged. This formula for the metric tensor g μ ν {displaystyle g_{mu u }!} is called the Kerr–Newman metric. It is a generalisation of the Kerr metric for an uncharged spinning point-mass, which had been discovered by Roy Kerr two years earlier.