Gravitational perturbations of the Schwarzschild spacetime: A Practical covariant and gauge-invariant formalism

By K. Martel, E. Poisson. 2005

256 citations recorded by the source corpus.

We present a formalism to study the metric perturbations of the Schwarzschild spacetime. The formalism is gauge invariant, and it is also covariant under two-dimensional coordinate transformations that leave the angular coordinates unchanged. The formalism is applied to the typical problem of calculating the gravitational waves produced by material sources moving in the Schwarzschild spacetime. We examine the radiation escaping to future null infinity as well as the radiation crossing the event horizon. The waveforms, the energy radiated, and the angular-momentum radiated can all be expressed in terms of two gauge-invariant scalar functions that satisfy one-dimensional wave equations. The first is the Zerilli-Moncrief function, which satisfies the Zerilli equation, and which represents the even-parity sector of the perturbation. The second is the Cunningham-Price-Moncrief function, which satisfies the Regge-Wheeler equation, and which represents the odd-parity sector of the perturbation. The covariant forms of these wave equations are presented here, complete with covariant source terms that are derived from the stress-energy tensor of the matter responsible for the perturbation.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bd9677c81a5ccce078a429796fde8f3b610eb0ad

How researchers see this paper

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In Astronomy and Astrophysics

1. András Vasy
2. Igor Rodnianski
3. Mihalis Dafermos
4. P. Hintz
5. S. Aretakis
6. B. Wardell
7. G. Holzegel
8. A. Pound

In Nuclear and High Energy Physics

1. András Vasy
2. Igor Rodnianski
3. P. Hintz
4. Mihalis Dafermos
5. S. Aretakis
6. B. Wardell
7. G. Holzegel
8. T. Binnington

Citations in the corpus

• Black hole perturbation theory and gravitational self-force (2021, background): “[116, 190] and can be transformed to the spin-weighted harmonic basis using similar relations.”
• The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “Recent studies of stability in the physics literature with an eye toward numerical implementation include [48, 61, 47].”
• Static response and Love numbers of Schwarzschild black holes (2020, methodology): “) See [89] for a nice discussion of these modes.”
• Relativistic theory of tidal Love numbers (2009, methodology): “The internal light-cone gauge is a modified version of the external gauge constructed by Preston and Poisson [8].”
• The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “The study was initiated in the seminal paper by Regge–Wheeler [RW57], with extensions by Vishveshwara [Vis70] and Zerilli [Zer70], analyzing metric perturbations of the Schwarzschild spacetime; a gauge-invariant formalism was introduced by Moncrief [Mon74], later extended to allow for coupling with ”