First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models

Abstract

We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological perturbations to satisfy constraints that link rotational and gravitational wave perturbations. We also prove that if the perturbation on the FLRW side vanishes identically, then the vacuole must be perturbatively static and hence Schwarzschild. By the dual nature of the problem, the first result translates into links between rotational and gravitational wave perturbations on a perturbed Oppenheimer-Snyder model, where the perturbed FLRW dust collapses in a perturbed Schwarzschild environment which rotates in equilibrium. The second result implies in particular that no region described by FLRW can be a source of the Kerr metric.

arXiv commentLaTeX; 29 pages

References in corpus (14)

• Second-order Perturbations of the Friedmann World Model
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• Perturbation of junction condition and doubly gauge-invariant variables
• Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior
• Gravitational Perturbations of Relativistic Membranes and Strings
• First and Second Order Perturbations of Hypersurfaces
• Symmetry-preserving matchings
• Axially symmetric Einstein-Straus models
• Cosmological perturbation theory, instantaneous gauges and local inertial frames
• Generalisation of the Einstein-Straus model to anisotropic settings
• Linear perturbations of matched spacetimes: the gauge problem and background symmetries
• Slowly rotating voids in cosmology
• Axially symmetric equilibrium regions of Friedmann-Lemaitre-Robertson-Walker universes
• Revisiting Rotational Perturbations and the Microwave Background

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• Cylindrically symmetric inhomogeneous dust collapse with a zero expansion component
• Gauge fixing and regularity of axially symmetric and axistationary second order perturbations around spherical backgrounds
• Quasi-Local Energy of a Rotating Object Described by Kerr Spacetime
• First order perturbations of hypersurfaces of arbitrary causal character