Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-05-08
Int.J.Geom.Meth.Mod.Phys.6:583-593,2009
Physics
High Energy Physics
High Energy Physics - Theory
13 pages. Section 6, with new original calculations, has been added, and the presentation has been improved
Scientific paper
10.1142/S0219887809003692
Electrodynamics in curved spacetime can be studied in the Eastwood--Singer gauge, which has the advantage of respecting the invariance under conformal rescalings of the Maxwell equations. Such a construction is here studied in Einstein spaces, for which the Ricci tensor is proportional to the metric. The classical field equations for the potential are then equivalent to first solving a scalar wave equation with cosmological constant, and then solving a vector wave equation where the inhomogeneous term is obtained from the gradient of the solution of the scalar wave equation. The Eastwood--Singer condition leads to a field equation on the potential which is preserved under gauge transformations provided that the scalar function therein obeys a fourth-order equation where the highest-order term is the wave operator composed with itself. The second-order scalar equation is here solved in de Sitter spacetime, and also the fourth-order equation in a particular case, and these solutions are found to admit an exponential decay at large time provided that square-integrability for positive time is required. Last, the vector wave equation in the Eastwood-Singer gauge is solved explicitly when the potential is taken to depend only on the time variable.
Esposito Giampiero
Roychowdhury Raju
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