Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass

Lydia Bieri; Piotr T. Chruściel

Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass

Gravitational Physics

Publications: Contribution to book › Chapter

Abstract

We present the argument that the past limit of the Trautman-Bondi mass is the ADM mass under weak hypotheses on the decay of the metric towards spatial infinity, without any smallness conditions on the initial data, assuming well defined energy, momentum, center of mass and angular moment. Part of the proof consists of a careful inspection of the proof of stability of Minkowski space-time, which is sketched. This is complemented by an interior gluing result for asymptotically flat initial data with well defined Poincar\'e charges, which is proved in detail.

Original language	English
Title of host publication	Nonlinear Analysis in Geometry and Applied Mathematics
Subtitle of host publication	Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications
Editors	Lydia Bieri, Piotr T. Chrusciel, Shing-Tung Yau
Place of Publication	Somerville, Massachusetts, U.S.A
Publisher	International Press
Pages	1-32
Number of pages	32
ISBN (Print)	9781571463449
Publication status	Published - 20 Oct 2017

Publication series

Series	Series in Mathematics
Volume	1

Austrian Fields of Science 2012

103028 Theory of relativity

Keywords

gr-qc

Access to Document

https://arxiv.org/abs/1612.04359

Cite this

Bieri, L., & Chruściel, P. T. (2017). Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass. In L. Bieri, P. T. Chrusciel, & S.-T. Yau (Eds.), Nonlinear Analysis in Geometry and Applied Mathematics: Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications (pp. 1-32). International Press. https://arxiv.org/abs/1612.04359

Bieri, Lydia ; Chruściel, Piotr T. / Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass. Nonlinear Analysis in Geometry and Applied Mathematics: Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications. editor / Lydia Bieri ; Piotr T. Chrusciel ; Shing-Tung Yau. Somerville, Massachusetts, U.S.A : International Press, 2017. pp. 1-32 (Series in Mathematics, Vol. 1).

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abstract = "We present the argument that the past limit of the Trautman-Bondi mass is the ADM mass under weak hypotheses on the decay of the metric towards spatial infinity, without any smallness conditions on the initial data, assuming well defined energy, momentum, center of mass and angular moment. Part of the proof consists of a careful inspection of the proof of stability of Minkowski space-time, which is sketched. This is complemented by an interior gluing result for asymptotically flat initial data with well defined Poincar\'e charges, which is proved in detail.",

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Bieri, L & Chruściel, PT 2017, Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass. in L Bieri, PT Chrusciel & S-T Yau (eds), Nonlinear Analysis in Geometry and Applied Mathematics: Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications. International Press, Somerville, Massachusetts, U.S.A, Series in Mathematics, vol. 1, pp. 1-32. <https://arxiv.org/abs/1612.04359>

Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass. / Bieri, Lydia; Chruściel, Piotr T.
Nonlinear Analysis in Geometry and Applied Mathematics: Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications. ed. / Lydia Bieri; Piotr T. Chrusciel; Shing-Tung Yau. Somerville, Massachusetts, U.S.A: International Press, 2017. p. 1-32 (Series in Mathematics, Vol. 1).

Publications: Contribution to book › Chapter

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AU - Bieri, Lydia

AU - Chruściel, Piotr T.

PY - 2017/10/20

Y1 - 2017/10/20

N2 - We present the argument that the past limit of the Trautman-Bondi mass is the ADM mass under weak hypotheses on the decay of the metric towards spatial infinity, without any smallness conditions on the initial data, assuming well defined energy, momentum, center of mass and angular moment. Part of the proof consists of a careful inspection of the proof of stability of Minkowski space-time, which is sketched. This is complemented by an interior gluing result for asymptotically flat initial data with well defined Poincar\'e charges, which is proved in detail.

AB - We present the argument that the past limit of the Trautman-Bondi mass is the ADM mass under weak hypotheses on the decay of the metric towards spatial infinity, without any smallness conditions on the initial data, assuming well defined energy, momentum, center of mass and angular moment. Part of the proof consists of a careful inspection of the proof of stability of Minkowski space-time, which is sketched. This is complemented by an interior gluing result for asymptotically flat initial data with well defined Poincar\'e charges, which is proved in detail.

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BT - Nonlinear Analysis in Geometry and Applied Mathematics

A2 - Bieri, Lydia

A2 - Chrusciel, Piotr T.

A2 - Yau, Shing-Tung

PB - International Press

CY - Somerville, Massachusetts, U.S.A

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Bieri L, Chruściel PT. Future-complete null hypersurfaces, interior gluings, and the Trautman-Bondi mass. In Bieri L, Chrusciel PT, Yau ST, editors, Nonlinear Analysis in Geometry and Applied Mathematics: Part of the program year 2015–2016 on “Nonlinear Equations” at the Harvard Center of Mathematical Sciences and Applications. Somerville, Massachusetts, U.S.A: International Press. 2017. p. 1-32. (Series in Mathematics, Vol. 1). Epub 2016 Dec 13.