Master Functions and Equations for Perturbations of Vacuum Spherically-Symmetric Spacetimes
arXiv:2108.08668 · doi:10.1103/PhysRevD.104.084053
Abstract
Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial tool to understand the dynamics of black hole perturbations. Spherical symmetry allows for an expansion of the perturbations in scalar, vector, and tensor harmonics. The resulting perturbative equations are decoupled for modes with different parity and different harmonic numbers. Moreover, for each harmonic and parity, the equations for the perturbations can be decoupled in terms of (gauge-invariant) master functions that satisfy 1+1 wave equations. By working in a completely general perturbative gauge, in this paper we study what is the most general master function that is linear in the metric perturbations and their first-order derivatives and satisfies a wave equation with a potential. The outcome of the study is that for each parity we have two branches of solutions with similar features. One of the branches includes the known results: In the odd-parity case, the most general master function is an arbitrary linear combination of the Regge-Wheeler and the Cunningham-Price-Moncrief master functions whereas in the even-parity case it is an arbitrary linear combination of the Zerilli master function and another master function that is new to our knowledge. The other branch is very different since it includes an infinite collection of potentials which in turn lead to an independent collection master of functions which depend on the potential. The allowed potentials satisfy a non-linear ordinary differential equation. Finally, all the allowed master functions are gauge invariant and can be written in a fully covariant form.
arXiv comment22 pages, revtex 4-2. (v2: title update) (v3: new conventions for a master function; update of a reference)
References in corpus (48)
- The Black Hole in Three Dimensional Space Time
- Quasinormal modes of black holes and black branes
- Quasi-Normal Modes of Stars and Black Holes
- Quasinormal modes of black holes: from astrophysics to string theory
- Physics, Astrophysics and Cosmology with Gravitational Waves
- Black holes, gravitational waves and fundamental physics: a roadmap
- The motion of point particles in curved spacetime
- Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
- A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
- Self-force and radiation reaction in general relativity
- The r-mode instability in rotating neutron stars
- Analytic black hole perturbation approach to gravitational radiation
- Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
- Extreme Gravity Tests with Gravitational Waves from Compact Binary Coalescences: (II) Ringdown
- Gravitational self force in extreme mass-ratio inspirals
- On the gravitational field of a mass point according to Einstein's theory
- Stability of Higher-Dimensional Schwarzschild Black Holes
- Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
- Toward Understanding CMB Anisotropies and Their Implications
- The linear stability of the Schwarzschild solution to gravitational perturbations
- Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes
- Quasi-Normal Modes and Gravitational Wave Astronomy
- Gauge-invariant gravitational perturbations of maximally symmetric spacetimes
- Black hole perturbation in the most general scalar-tensor theory with second-order field equations I: The odd-parity sector
- Black hole perturbation in the most general scalar-tensor theory with second-order field equations II: the even-parity sector
- Black Hole Perturbation
- Covariant Perturbations of Schwarzschild Black Holes
- Entropies of Scalar Fields on Three Dimensional Black Holes
- Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates
- Gauge-invariant and coordinate-independent perturbations of stellar collapse I: the interior
- Second order perturbations of a Schwarzschild black hole
- Head-on collisions of black holes: the particle limit
- Gravitational radiation from Schwarzschild black holes: the second order perturbation formalism
- The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
- The structure of the extreme Schwarzschild-de Sitter space-time
- Second and higher-order perturbations of a spherical spacetime
- NR/HEP: roadmap for the future
- Schwarzschild and Birkhoff a la Weyl
- A simple proof of Birkhoff's theorem for cosmological constant
- Gauge-invariant and coordinate-independent perturbations of stellar collapse II: matching to the exterior
- Superradiance -- the 2020 Edition
- Quasinormal modes as a distinguisher between general relativity and f(R) gravity
- Non-Linear N-Parameter Spacetime Perturbations: Gauge Transformations
- Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes
- Darboux Covariance: A Hidden Symmetry of Perturbed Schwarzschild Black Holes
- Quasinormal modes as a distinguisher between general relativity and f(R) gravity: Charged black-holes
- Distinguishing general relativity from Chern-Simons gravity using gravitational wave polarizations
- Improvement on the metric reconstruction scheme in the Regge-Wheeler-Zerilli formalism
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- Darboux Covariance: A Hidden Symmetry of Perturbed Schwarzschild Black Holes
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- EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
- On the propagation of gravitational waves in matter-filled Bianchi I universe
- Spectral Problems for Quasinormal Modes of Black Holes