A covariant approach for perturbations of rotationally symmetric spacetimes

Abstract

We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3 covariant approach to perturbation theory in cosmology, the semi-tetrad, 1+1+2 approach presented here should be useful for analysing perturbations of a variety of systems in a covariant and gauge-invariant manner. Such applications range from stellar objects to cosmological models such as the spherically symmetric Lemaitre-Tolman-Bondi solutions or the class of locally rotationally symmetric Bianchi models.

arXiv comment13 pages

References in corpus (8)

• Covariant Perturbations of Schwarzschild Black Holes
• The Covariant Approach to LRS Perfect Fluid Spacetime Geometries
• Cosmic microwave background anisotropies in the CDM model: a covariant and gauge-invariant approach
• Cosmic microwave background anisotropies: Nonlinear dynamics
• Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes
• A covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations
• The electromagnetic signature of black hole ringdown
• Incorporation of Spacetime Symmetries in Einstein's Field Equations

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