Covariant Schwarzschild perturbations. I: Initial value formulation for scalars of spin-weight +- 2

Nov, 2006
17 pages
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20072011201520192023410
Abstract: (arXiv)
We consider full perturbations to a covariantly defined Schwarzschild spacetime. By constructing complex quantities, we derive two decoupled, covariant and gauge-invariant, wave-like equations for spin-weighted scalars. These arise naturally from the Bianchi identities and comprise a covariant representation of the Bardeen-Press equations for scalars with spin-weight ±2\pm2. Furthermore, the covariant and gauge-invariant 1+1+2 formalism is employed, and consequently, the physical interpretation of the energy-momentum perturbations is transparent. They are written explicitly in terms of the energy-momentum specified on spacelike three-slices. Ultimately, a Cauchy problem is constructed whereby, an initial three-slice may be perturbed by an energy-momentum source, which induces resultant gravitational fields.
Note:
  • Submitted to Class.Quant.Grav.
  • 04.25.Nx
  • 04.30.Db
  • 04.20.Cv
  • 04.20.Ex
  • 04.20.-q
  • 04.30.-w
  • space-time: Schwarzschild
  • tensor: energy-momentum
  • Bianchi identity
  • decoupling