Gravitational Perturbations of Rotating Black Holes in Lorenz Gauge

Dolan, Sam R.; Kavanagh, Chris; Wardell, Barry

doi:10.1103/physrevlett.128.151101

Cited by 22 publications

(13 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further development is also needed for scenarios with matter distributions, where the wave equations for density fluctuations couple with the gravitational waves degrees of freedom [118,127]. Overall, we do not anticipate any conceptual difficulty in extending the framework to a system of coupled wave equations when they all share the same characteristic speed of propagation, such as the formulations common to the gravitational selfforce programme [124][125][126]128,129]. The framework is also applicable to a system of coupled wave equations with varying propagation speeds due to matter distributions, but a more careful analysis of the solutions' regularity properties might be needed.…”

Section: Discussionmentioning

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.

View full text Add to dashboard Cite

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’.

show abstract

Section: Discussionmentioning

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.

View full text Add to dashboard Cite

show abstract

“…In Lorenz gauge, equation (2) reduces to a wave equation in manifestly hyperbolic form, which is a desirable feature for many applications. The question of how to find a metric perturbation in Lorenz gauge on Kerr spacetime in a way that builds on the approach of Teukolsky was recently addressed in [16]; here we extend and build on that work to develop a fully-fledged calculational scheme.…”

Section: Introductionmentioning

confidence: 99%

“…• Osburn and Nishimura [57] have used a scalar-field toy model to propose that it may be feasible to directly compute the metric perturbation by solving a set of 2D elliptic partial differential equations in the (r, θ) domain; • Aksteiner et al (AAB) [58] have shown that, by combining the two maximum-spin components of the Weyl tensor, a Hertz-potential approach can be used in the presence of sources without introducing a corrector tensor; • Dolan et al [16] showed that, in vacuum regions, the radiation-gauge metric perturbation arising from the CCK procedure can be transformed into the Lorenz gauge by using a gauge vector that is straightforwardly obtained from solutions of the Teukolsky equation.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we continue the development of the last approach [16], by seeking to construct a Lorenz-gauge metric perturbation for a canonical non-vacuum case. More specifically, in the following sections we will calculate the linearised metric perturbation h (1) µν (henceforth omitting the superscript) for the special case of a particle on a circular equatorial orbit of Kerr spacetime, by solving the system…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Metric perturbations of Kerr spacetime in Lorenz gauge: circular equatorial orbits

Dolan,

Durkan,

Kavanagh

et al. 2024

Class. Quantum Grav.

View full text Add to dashboard Cite

We construct the metric perturbation in Lorenz gauge for a compact body on a circular equatorial orbit of a rotating black hole (Kerr) spacetime, using a newly-developed method of separation of variables. The metric perturbation is formed from a linear sum of differential operators acting on Teukolsky mode functions, and certain auxiliary scalars, which are solutions to {\it ordinary} differential equations in the frequency domain. For radiative modes, the solution is uniquely determined by the $s=\pm2$ Weyl scalars, the $s=0$ trace, and $s=0,1$ gauge scalars whose amplitudes are determined by imposing continuity conditions on the metric perturbation at the orbital radius. The static (zero-frequency) part of the metric perturbation, which is handled separately, also includes mass and angular momentum completion pieces. The metric perturbation is validated against the independent results of a 2+1D time domain code, and we demonstrate agreement at the expected level in all components, and the absence of gauge discontinuities. In principle, the new method can be used to determine the Lorenz-gauge metric perturbation at a sufficiently high precision to enable accurate second-order self-force calculations on Kerr spacetime in future. We conclude with a discussion of extensions of the method to eccentric and non-equatorial orbits.

show abstract

“…Handling arbitrary matter sources was approached in [53], through the use of a correction term to make sure that the constructed metric perturbation satisfies the linearized Einstein field equations. Moreover, in [54] a parallel method in Lorenz gauge to the CCKW was recently introduced that overcomes those obstacles brought by the radiation gauges. Moreover, this is not the only way around the CCKW, In [55], in ORG the researchers constructed the metric directly without intermediate Hertz-like potentials.…”

Section: Introductionmentioning

confidence: 99%

In horizon penetrating coordinates: Kerr black hole metric perturbation, construction and completion

Aly,

Stojkovic

2023

Class. Quantum Grav.

View full text Add to dashboard Cite

We investigate the Teukolsky equation in horizon-penetrating coordinates to study the behavior of perturbation waves crossing the outer horizon. For this purpose, we use the null ingoing/outgoing Eddington-Finkelstein coordinates. The first derivative of the radial equation is a Fuchsian differential equation with an additional regular singularity to the ones the radial one has. The radial functions satisfy the physical boundary conditions without imposing any regularity conditions. We also observe that the Hertz-Weyl scalar equations preserve their angular and radial signatures in these coordinates. Using the angular equation, we construct the metric perturbation for a circularly orbiting perturber around a black hole in Kerr spacetime in a horizon-penetrating setting. Furthermore, we completed the missing metric pieces due to the mass $M$ and angular momentum $J$ perturbations. We also provide an explicit formula for the metric perturbation as a function of the radial part, its derivative, and the angular part of the solution to the Teukolsky equation. Finally, we discuss the importance of the extra singularity in the radial derivative for the convergence of the metric expansion.

show abstract

Gravitational Perturbations of Rotating Black Holes in Lorenz Gauge

Cited by 22 publications

References 55 publications

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

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

Metric perturbations of Kerr spacetime in Lorenz gauge: circular equatorial orbits

In horizon penetrating coordinates: Kerr black hole metric perturbation, construction and completion

Contact Info

Product

Resources

About