The Electromagnetic Signature of Black Hole Ring‐Down

Clarkson, Chris; Marklund, Mattias; Betschart, Gerold; Dunsby, Peter K. S.

doi:10.1086/422497

Cited by 46 publications

(71 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The vectors and tensors can be also expanded in harmonics by introducing the vector and tensor spherical harmonics [56,57,59]. The even (electric) and odd (magnetic) parity vector harmonics are 41) and the vector Ψ a can be expanded as…”

Section: Harmonic Expansionmentioning

confidence: 99%

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Keresztes

Forsberg

Bradley

et al. 2015

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

Abstract. A general treatment of vorticity-free, perfect fluid perturbations of KantowskiSachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by π/2 and share the same speed of sound.

show abstract

Section: Harmonic Expansionmentioning

confidence: 99%

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Keresztes

Forsberg

Bradley

et al. 2015

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

show abstract

“…For completeness we also give the decomposition of Maxwell's equations, previously given in [10]. We decompose the electric and magnetic field vectors as…”

Section: E Maxwell's Equationsmentioning

confidence: 99%

“…This tensor contains in compact form the curved space generalisation of the two flat space GW polarizations h + and h × [10] (see also [11] for an extension of this work). The approach here also been used to study scalar and electromagnetic perturbations of LRS spacetimes, and generalised Regge-Wheeler equations were found [12,13].…”

Section: Introductionmentioning

confidence: 99%

Covariant approach for perturbations of rotationally symmetric spacetimes

2007

View full text Add to dashboard Cite

We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -and general locally rotationally symmetric -spacetimes. Based upon the utility of the 1+3 covariant approach to perturbation theory in cosmology, the semitetrad, 1+1+2 approach presented here should be useful for analysing perturbations of a variety of systems in a covariant and gauge-invariant manner. Such applications range from stellar objects to cosmological models such as the spherically symmetric Lemaître-Tolman-Bondi solutions or the class of locally rotationally symmetric Bianchi models.

show abstract

“…In Section 3, EM perturbations on arbitrary LRS space-times are considered and the corresponding first-order Maxwell equations in 1+1+2 form are reproduced from [8]. Subsequently, we use eigenvalue/eigenvector analysis to reveal that a very natural way to decouple the 1+1+2 Maxwell equations is to construct new complex dependent variables.…”

Section: Introductionmentioning

confidence: 99%

1+1+2 electromagnetic perturbations on general LRS spacetimes: Regge–Wheeler and Bardeen–Press equations

Burston

Lun

2008

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett [1], and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS spacetimes, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations.

show abstract

The Electromagnetic Signature of Black Hole Ring‐Down

Cited by 46 publications

References 47 publications

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Gravitational, shear and matter waves in Kantowski-Sachs cosmologies

Covariant approach for perturbations of rotationally symmetric spacetimes

1+1+2 electromagnetic perturbations on general LRS spacetimes: Regge–Wheeler and Bardeen–Press equations

Contact Info

Product

Resources

About