Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with $l\ge 2$

Abstract

In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaître-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.

arXiv comment16 pages, 4 figures

References in corpus (17)

• Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes
• Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates
• Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
• All nonspherical perturbations of the Choptuik spacetime decay
• Gravitational Radiation from a Naked Singularity -- Odd-Parity Perturbation --
• Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field
• Gravitational Radiation from a Naked Singularity. II - Even-Parity Perturbation -
• Dynamical extensions for shell-crossing singularities
• Critical gravitational collapse of a perfect fluid: nonspherical perturbations
• Critical Collapse Beyond Spherical Symmetry: General Perturbations of the Roberts Solution
• Spacetime structure of self-similar spherically symmetric perfect fluid solutions
• Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation
• Geometry and topology of singularities in spherical dust collapse
• Cauchy horizon stability in self-similar collapse: scalar radiation
• Even perturbations of self-similar Vaidya space-time
• Bounds for scalar waves on self-similar naked-singularity backgrounds
• The stability of Killing-Cauchy horizons in colliding plane wave space-times

Cited by in corpus (3)

• Shadow of a naked singularity
• Odd Parity Perturbations of the Self-Similar LTB Spacetime
• Cauchy horizon stability in a collapsing spherical dust cloud. II: Energy bounds for test fields and odd-parity gravitational perturbations