Abstract
In this review we present the most general form of the Janis–Newman algorithm. This extension allows generating configurations which contain all bosonic fields with spin less than or equal to two (real and complex scalar fields, gauge fields, metric field) and with five of the six parameters of the Plebański–Demiański metric (mass, electric charge, magnetic charge, NUT charge and angular momentum). Several examples are included to illustrate the algorithm. We also discuss the extension of the algorithm to other dimensions.
Highlights
General relativity is the theory of gravitational phenomena
As explained in the previous section, the JN algorithm was formulated only for the metric and all other fields had to be found using the equations of motion
For example neither the Kerr–Newman gauge field or its associated field strength could be derived in [4]. The solution to this problem is to perform a gauge transformation in order to remove the radial component of the gauge field in null coordinates [57]
Summary
General relativity is the theory of gravitational phenomena It describes the dynamical evolution of spacetime through the Einstein–Hilbert action that leads to Einstein equations. As the complexity of the equations of motion increase, it is harder to find exact analytical solutions, and one often consider specific types of solutions (extremal, BPS), truncations (some fields are constant, equal or vanishing) or solutions with restricted number of charges. For this reason it is interesting to find solution generating algorithms – procedures which transform a seed configuration to another configuration with a greater complexity (for example with a higher number of charges). Even if in practice this kind of solution generating technique does not provide so many new solutions, it can help to understand better the underlying theory (which can be general relativity, modified gravities or even supergravity) and it may shed light on the structure of gravitational solutions
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