2006/11/08 by Raymond Burston, R. B. Burston, Burston, R. B. +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0611052
17 pages. Submitted to Class. Quantum Grav
arxiv created 2006/11/08 · openalex publication_date 2006/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. 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.