Linearization instability of gravity waves?
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Gravity waves in irrotational dust spacetimes are characterized by a nonzero magnetic Weyl tensor Hab. In the linearized theory, the divergence of Hab is set to zero. Recently Lesame, Ellis, and Dunsby [Phys. Rev. D 53, 738 (1996)] presented an argument to show that, in the exact nonlinear theory, divH=0 forces Hab=0, thus implying a linearization instability for gravity waves interacting with matter. However a sign error in the equations invalidates their conclusion. Bianchi type V spacetimes are shown to include examples with divH=0≠Hab. An improved covariant formalism is used to show that in a generic irrotational dust spacetime the covariant constraint equations are preserved under evolution. It is shown elsewhere that divH=0 does not generate further conditions. [S0556-2821(97)03502-9]
|Journal||Physical Review D|
|Publication status||Published - 15 Jan 1997|