A new look at the Bondi-Sachs energy-momentum

Frauendiener, Jörg; Stevens, Chris

doi:10.48550/arxiv.2104.13646

Cited by 3 publications

(9 citation statements)

References 22 publications

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“…We observe a particular oscillating behaviour of the gravitational field which seems to be related to the onset of quasi-normal ringing. We also verify numerically that the Bondi-Sachs massloss formula is satisfied in our simulation by computing the relevant asymptotic quantities directly on I + based on the general expressions for the Bondi-Sachs energy-momentum, news and flux derived in a recent paper [10]. This provides a strong check on the accuracy of our numerical computations.…”

supporting

confidence: 55%

“…In this section we summarize the results obtained in [10] and put forward the analytical expressions required to compute the Bondi-Sachs energy on arbitrary cuts of I + .…”

Section: The Bondi-sachs Componentsmentioning

confidence: 99%

“…So then, how does one who has run a numerical evolution that includes I in the computational domain actually compute the correct quantities? In a recent paper [10] we discuss this question and derive expressions for the Bondi-Sachs energy-momentum and the gravitational flux which are valid on arbitrary cuts and for any choice of coordinates, frame and conformal factor.…”

Section: Introductionmentioning

confidence: 99%

“…The layout of the paper is as follows: section 2 provides a summary the IBVP framework for the GCFE while in section 4 we describe the specifics of the system to be evolved. Section 3 describes how we make use of the formula for the Bondi components given in [10] and section 7 presents the numerical results. The paper is concluded with a brief discussion and a summary in section 8.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

Frauendiener¹,

Stevens²

2021

Class. Quantum Grav.

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Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity. Although being an attractive option for studying global quantities by way of local differential geometrical methods, how viable are the GCFE for study of quantities arising in the physical space-time? In particular, how long can the evolution track phenomena that need a constant proper physical timestep to be accurately resolved? We address this question by studying the curvature oscillations induced on the Schwarzschild spacetime by a non-linear gravitational perturbation. For small enough amplitudes, these are the well approximated by the linear quasinormal modes, where each mode rings at a frequency determined solely by the Schwarzschild mass. We find that the GCFE can indeed resolve these oscillations, which quickly approach the linear regime, but only for a short time before the compactification becomes "too fast" to handle numerically.

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supporting

confidence: 55%

“…In this section we summarize the results obtained in [10] and put forward the analytical expressions required to compute the Bondi-Sachs energy on arbitrary cuts of I + .…”

Section: The Bondi-sachs Componentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

Frauendiener¹,

Stevens²

2021

Class. Quantum Grav.

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“…(III.50) is presented including the matter term and the factors associated to the choice of foliation Ḟ and translation α; in the literature, either just eq. (III.49) is given [16], even without the matter contribution (see [50] for a recent derivation), or just eq. (III.50) is considered, typically without the matter term nor the factor Ḟ corresponding to the choice of foliation [28,51,52].…”

Section: Iiic Asymptotic Energy-momentum Of the Gravitational Fieldmentioning

confidence: 99%

Asymptotic Structure with vanishing cosmological constant

Fernández-Álvarez,

Senovilla

2021

Preprint

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This is the first of two papers [1] devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant Λ. This first paper is concerned with the case of Λ = 0. Our approach is fully based on the tidal nature of the gravitational field and therefore on the 'tidal energies' built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with Λ > 0 covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of supertranslation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

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Asymptotic structure with vanishing cosmological constant

Fernández-Álvarez¹,

Senovilla²

2022

Class. Quantum Grav.

View full text Add to dashboard Cite

This is the first of two papers [1] devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant Λ. This first paper is concerned with the case of Λ = 0. Our approach is fully based on the tidal nature of the gravitational field and therefore on the ‘tidal energies’ built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with Λ > 0 covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super- translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

show abstract

A new look at the Bondi-Sachs energy-momentum

Cited by 3 publications

References 22 publications

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

The non-linear perturbation of a black hole by gravitational waves. I. The Bondi–Sachs mass loss

Asymptotic Structure with vanishing cosmological constant

Asymptotic structure with vanishing cosmological constant

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