2021/04/30 by Jörg Frauendiener, Chris Stevens · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Curvature #Energy–momentum relation #Formalism (music) #Geometry #Invariant (physics) #Invariant mass #Mathematical physics #Mathematics #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Theoretical physics #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/ac3e4f
published in Classical and Quantum Gravity 39(2), 025007 (IOP Publishing) · 23 pages, typos removed, one reference added. Another reference added, clarifying text added in two places
arxiv created 2021/07/31 · openalex publication_date 2021/11/29 · arxiv updated 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract How does one compute the Bondi mass on an arbitrary cut of null infinity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">I</mml:mi> </mml:math> when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi–Sachs energy–momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">I</mml:mi> </mml:math> so that most of the available formulations of the Bondi energy–momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy–momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the ‘co-curvature’, a naturally appearing quantity closely related to the Gauß curvature on a cut of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi mathvariant="script">I</mml:mi> </mml:math> .