Energy- and angular momentum-like Noether currents for the Teukolsky Master Equation

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Written by Gabor Zsolt Toth

Conserved currents associated with the time translation and axial symmetries of the Kerr spacetime
are constructed for the Teukolsky Master Equation (TME). Three partly different approaches are discussed,
in which three variants of Noether's theorem are applied. The three approaches give essentially the same results, nevertheless. The first approach provides an example of the application of an extension of Noether's theorem to nonvariational differential equations. The variant of Noether's theorem applied in the third approach is a generalization of the standard construction of conserved currents associated with spacetime symmetries in general relativity, in which the currents are obtained as the contraction of the symmetric energy-momentum tensor with the relevant Killing vector fields. The constructed currents involve two independent solutions of the TME with opposite spin weights.