New form of the Kerr-Newman solution

A new form of the Kerr-Newman solution is presented. The solution involves a time coordinate which represents the local proper time for a charged massive particle released from rest at spatial infinity. The chosen coordinates ensure that the solution is well-behaved at horizons and enable an intuitive description of many physical phenomena. If the charge of the particle e = 0, the coordinates reduce to Doran coordinates for the Kerr solution with the replacement M - M - Q2=(2r), where M and Q are the mass and charge of the black hole, respectively. Such coordinates are valid only for r >= Q2=(2M), however, which corresponds to the region that a neutral particle released from rest at infinity can penetrate. By contrast, for e not equal 0 and of opposite sign to Q, the new coordinates have a progressively extended range of validity as lel increases and tend to advanced Eddington-Finkelstein (EF) null coordinates as lel - infinity, hence becoming global in this limit. The Kerr solution (i.e. with Q = 0) may also be written in terms of the new coordinates by setting eQ = -alpha, where alpha is a real parameter unrelated to charge; in this case the coordinate system is global for all non-negative values of alpha and the limits alpha = 0 and alpha - infinity correspond to Doran coordinates and advanced EF null coordinates, respectively, without any need to transform between them.

Automated summary

A new form of the Kerr-Newman solution is discussed, which uses a time coordinate to represent the proper time for a charged massive particle released from rest at infinity. The chosen coordinates ensure the well-behaved behavior of the solution at horizons and provide an intuitive description of various physical phenomena.