Gauge invariant perturbations of general spherically symmetric spacetimes

Li, Wentao; Fang, Xiongjun; Jing, Jiliang; Wang, Anzhong

doi:10.1007/s11433-022-1956-4

Cited by 21 publications

(6 citation statements)

References 48 publications

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“…A similar analysis using the metric perturbation was performed in [17][18][19], where the wave equations resembled the Regge-Wheeler and the Zerilli equations [20,21], and its generalization to general spin s has also been studied [22]. In the vacuum case, there is a transformation between the Teukolsky and Regge-Wheeler equations, known as the Chandrasekhar transformation [23].…”

Section: Summary and Discussionmentioning

confidence: 99%

Teukolsky-like equations with various spins in spherically symmetric spacetime*

Guo 郭,

Nakajima,

Lin 林

2024

Chinese Phys. C

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Section: Summary and Discussionmentioning

confidence: 99%

Teukolsky-like equations with various spins in spherically symmetric spacetime*

Guo 郭,

Nakajima,

Lin 林

2024

Chinese Phys. C

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“…To exemplify the effects of the hyperboloidal coordinates on the perturbation equations for black-hole perturbation theory, we consider scenarios in which the dynamics of the fields are reducible to a single master equation of the form −Ψ,tt+Ψ,r∗r∗−Vfalse(rfalse)Ψ=Rfalse(rfalse).The potential Vfalse(rfalse) is assumed to vanish as r∗false→±normal∞. We recall that the equation (3.1) is not necessarily the most generic expression to describe perturbations over spherically symmetric spacetimes, with line element of the form (2.1) as discussed, for instance, in Liu et al [117] and Cardoso et al [118]. However, equation (3.1) applies for a wide range of scenarios with spherical symmetry, and it provides us with a useful proxy for understanding how to apply the hyperboloidal methods in black-hole perturbation theory.…”

Section: Black-hole Perturbation Theorymentioning

confidence: 99%

Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics

Panosso Macedo

2024

Phil. Trans. R. Soc. A.

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This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the Trautman–Bondi mass in terms of the hyperboloidal metric functions. Moreover, we apply this formalism to a class of wave equations commonly used in black-hole perturbation theory. Additionally, we provide a comprehensive derivation of the hyperboloidal minimal gauge, introducing two alternative approaches within this conceptual framework: the in-out and out-in strategies. Specifically, we demonstrate that the height function in the in-out strategy follows from the well-known tortoise coordinate by changing the sign of the terms that become singular at future null infinity. Similarly, for the out-in strategy, a sign change also occurs in the tortoise coordinate’s regular terms. We apply the methodology to the following spacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensional black holes, black hole with matter halo, and Reissner–Nordström–de Sitter. From this heuristic study, we conjecture that the out-in strategy is best adapted for black hole geometries that account for environmental or effective quantum effects. This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.

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“…mass ratio inspiral problems for Bardeen (Anti-)de Sitter black holes. As such, the complete basis on the twosphere is constructed by a 1-scalar spherical harmonic, , three pure-spin vector harmonics, and six tensor harmonics [37]. The vector harmonics are defined as…”

Section: Bardeen (Anti-) De Sitter Black Holementioning

confidence: 99%

Quasinormal modes and isospectrality of Bardeen (Anti-) de Sitter black holes*

Zhao 赵,

Liu 刘,

Zhang 张

et al. 2024

Chinese Phys. C

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Black holes (BHs) exhibiting coordinate singularities but lacking essential singularities throughout the entire spacetime are referred to as regular black holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who considered the Einstein equation coupled with a nonlinear electromagnetic field. In this study, we investigate the gravitational perturbations, including the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We derive the master equations with source terms for both axial and polar perturbations, and subsequently compute the quasinormal modes (QNMs) through numerical methods. For the Bardeen de Sitter black hole, we employ the 6th-order WKB approach. The numerical results reveal that the isospectrality is broken in this case. Conversely, for Bardeen Anti-de Sitter black holes, the QNM frequencies are calculated by using the HH method.

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Gauge invariant perturbations of general spherically symmetric spacetimes

Cited by 21 publications

References 48 publications

Teukolsky-like equations with various spins in spherically symmetric spacetime*

Teukolsky-like equations with various spins in spherically symmetric spacetime*

Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics

Quasinormal modes and isospectrality of Bardeen (Anti-) de Sitter black holes*

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