The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

Frauendiener, Jörg; Goodenbour, Alex; Stevens, Christian V.

doi:10.48550/arxiv.2301.05268

Cited by 1 publication

(1 citation statement)

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“…The formalism is particularly useful in numerical relativity as it allows the formulation of Einstein's equations as a Cauchy problem: given adequate initial and boundary conditions, the equations fully determine the future evolution of the system [90][91][92][93][94]. The nonlinear evolution of Einstein's equation in the hyperboloidal formalism has undergone great progress in the past years (see for instance, [95][96][97][98][99][100][101][102][103][104][105][106] and references therein), but several challenges remain open (e.g. binary black-hole evolutions).…”

Section: (V) 3 + 1 Representationmentioning

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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Section: (V) 3 + 1 Representationmentioning

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

The non-linear perturbation of a black hole by gravitational waves. III. Newman-Penrose constants

Cited by 1 publication

References 23 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

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