High-order perturbations of a spherical collapsing star

Abstract

In Ref. [1, 2] a formalism to deal with high-order perturbations of a general spherical background was developed. In this article, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density and velocity. In general, these expressions are not linear and have sources depending on lower order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular the surface separating the perfect fluid interior from the exterior vacuum.

21 pages

References in corpus (30)

• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
• The motion of point particles in curved spacetime
• Phenomenological template family for black-hole coalescence waveforms
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Gravitational waves and pulsating stars: What can we learn from future observations?
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• xPert: Computer algebra for metric perturbation theory
• Accurate Effective-One-Body waveforms of inspiralling and coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
• Black-hole binary simulations: the mass ratio 10:1
• Oscillations of rapidly rotating relativistic stars
• A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
• Perturbation of junction condition and doubly gauge-invariant variables
• Second and higher-order perturbations of a spherical spacetime
• Oscillations and instabilities of fast and differentially rotating relativistic stars
• Intermediate Mass Ratio Black Hole Binaries: Numerical Relativity meets Perturbation Theory
• Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior
• High-order gauge-invariant perturbations of a spherical spacetime
• First and Second Order Perturbations of Hypersurfaces
• Nonradial oscillations of slowly and differentially rotating compact stars
• Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation
• Nonlinear radial oscillations of neutron stars
• Current status of Japanese detectors
• Non-axisymmetric oscillations of differentially rotating relativistic stars
• Linear perturbations of matched spacetimes: the gauge problem and background symmetries
• A comparison of methods for gravitational wave burst searches from LIGO and Virgo

Cited by in corpus (9)

• xPand: An algorithm for perturbing homogeneous cosmologies
• NR/HEP: roadmap for the future
• Linear perturbations of self-gravitating spherically symmetric configurations
• Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass
• Completion of the universal I-Love-Q relations in compact stars including the mass
• A generalization of the Zerilli master variable for a dynamical spherical spacetime
• Gauge fixing and regularity of axially symmetric and axistationary second order perturbations around spherical backgrounds
• xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes
• First order perturbations of hypersurfaces of arbitrary causal character