Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior

Abstract

In Paper I in this series we constructed evolution equations for the complete gauge-invariant linear perturbations of a time-dependent spherically symmetric perfect fluid spacetime. A key application of this formalism is the interior of a collapsing star. Here we derive boundary conditions at the surface of the star, matching the interior perturbations to the well-known perturbations of the vacuum Schwarzschild spacetime outside the star.

18 pages, RevTex

Cited by in corpus (43)

• Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
• The linear stability of the Schwarzschild solution to gravitational perturbations
• Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes
• Extraction of Gravitational Waves in Numerical Relativity
• The rotational modes of relativistic stars: Numerical results
• Gravitational Waves from Nonlinear Couplings of Radial and Polar Nonradial Modes in Relativistic Stars
• Second and higher-order perturbations of a spherical spacetime
• Coupling of Radial and Axial non-Radial Oscillations of Compact Stars: Gravitational Waves from first-order Differential Rotation
• Gravitational-Wave Extraction from Neutron Star Oscillations: comparing linear and nonlinear techniques
• On the accretion-induced QNM excitation of a Schwarzschild black hole
• Accretion-driven gravitational radiation from nonrotating compact objects. Infalling quadrupolar shells
• First and Second Order Perturbations of Hypersurfaces
• Coupling of radial and non-radial oscillations of relativistic stars: gauge-invariant formalism
• Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation
• Gravitational waves from pulsations of neutron stars described by realistic Equations of State
• WKB metastable quantum states of a de Sitter--Reissner-Nordstroem dust shell
• Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results
• Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass
• Physical interpretation of gauge invariant perturbations of spherically symmetric space-times
• Linear perturbations of matched spacetimes: the gauge problem and background symmetries
• Hamiltonian theory for the axial perturbations of a dynamical spherical background
• Construction of gauge-invariant variables of linear metric perturbations on an arbitrary background spacetime
• Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order
• Gravitational radiation from collapsing magnetized dust
• High-order perturbations of a spherical collapsing star
• First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models
• Perturbations of relativistic dissipative stars
• Proposal of a gauge-invariant treatment of l=0,1-mode perturbations on Schwarzschild Background Spacetime
• Covariant Perturbations of f(R) Black Holes: The Weyl Terms
• Gravitational Radiation from Collapsing Magnetized Dust. II -- Polar Parity Perturbation --
• Evolution of linear perturbations in Lemaître-Tolman-Bondi void models
• A generalization of the Zerilli master variable for a dynamical spherical spacetime
• EZ gauge is singular at the event horizon
• Review on the matching conditions for the tidal problem: towards the application to more general contexts
• Gauge-invariant perturbations of relativistic non-perfect fluids in spherical spacetime
• Master Functions and Equations for Perturbations of Vacuum Spherically-Symmetric Spacetimes
• Perturbation theory of spherically symmetric self-similar black holes
• Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part III: -- Realization of exact solutions
• Non-linear Oscillations of Compact Stars and Gravitational Waves
• Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part I : -- Formulation and odd-mode perturbations
• Gauge-invariant perturbation theory on the Schwarzschild background spacetime Part II: -- Even-mode perturbations