Teukolsky Master Equation: De Rham wave equation for the gravitational and electromagnetic fields in vacuum

Abstract

A new version of the Teukolksy Master Equation, describing any massless field of different spin $s=1/2,1,3/2,2$ in the Kerr black hole, is presented here in the form of a wave equation containing additional curvature terms. These results suggest a relation between curvature perturbation theory in general relativity and the exact wave equations satisfied by the Weyl and the Maxwell tensors, known in the literature as the de Rham-Lichnerowicz Laplacian equations. We discuss these Laplacians both in the Newman-Penrose formalism and in the Geroch-Held-Penrose variant for an arbitrary vacuum spacetime. Perturbative expansion of these wave equations results in a recursive scheme valid for higher orders. This approach, apart from the obvious implications for the gravitational and electromagnetic wave propagation on a curved spacetime, explains and extends the results in the literature for perturbative analysis by clarifying their true origins in the exact theory.

30 pages. No figures. Used PTP macros. To appear on Prog. Theor. Phys., Vol. 107, No. 5, May 2002

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