摘要
广义相对论中,引力波是具波的形式并且辐射能量的真空时空度量,而Bondi-Sachs度量是这类度量的自然描述之一.本文将概述零宇宙常数时Bondi-Sachs度量的Bondi能量动量非负性定理、Bondi能量动量和ADM(Arnowitt-Deser-Misner)能量动量的关系,以及非零宇宙常数时BondiSachs度量的一类自然边值条件及其在该边值条件下的peeling性质、B-引力波的一些新特性.
In general relativity, gravitational waves are wave-like metrics which radiate energy, and Bondi-Sachs metrics are one of natural metrics describing them. In this paper, we provide a short review on positivity of the Bondi energy-momentum and the relation between the Bondi energy-momentum and the ADM energy-momentum for Bondi-Sachs metrics when the cosmological constant is zero. We also review a natural boundary condition of the Bondi-Sachs metrics when the cosmological constant is nonzero, and present the peeling property as well as some new features of gravitational B-waves under this boundary condition.
引文
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1)It is believed that when a star has exhausted all thermonuclear sources of energy,it will collapse under its own gravitational field.Oppenheimer and Snyder10have given a rigorous study of the process for a spherically symmetric dust cloud by using a special solution given by Tolman11,in the restricted case of a spatially constant matter density starting from rest.This study was taken anew by Gu Chao Hao12,in a study of the Tolman solution,but not restricted to spatially constant matter.Gu Chao Hao gave an analysis of shell crossing singularities as well as the essential singularity at the centre of symmetry.He gave a detailed mathematical discussion of the formation of horizons and of what is now called the nakedness of these singularities.Hu Hesheng13constructed the complete solutions of the fully general spherically symmetric solution for dust,not restricted to the Tolman class,and discussed their properties.The work done by Gu Chao Hao and Hu Hesheng for non-homogeneous dust clouds was done again,unaware of these papers published in China,by Mu¨ller zum Hagen,Seifert,and Yodzis14(Tolman class,shell crossing singularities),Christodoulou15(starting from rest,central singularities)and Richard Newman16(general solution).These western papers were motivated by the cosmic censorship conjecture,which is violated both at“shell crossing”singularities and at the centre,as was already shown in Gu’s paper.10 Oppenheimer,J.R.and Snyder,H.(1939)Phys.Rev.56,455.11 Tolman,R.(1934)Proc.Natl.Acad.Sci.USA,20,169-76,Bondi,H.(1947)Mon.Nat.R.Astron.Soc.,107,410-25.12 Gu Chao Hao(1973)J.Fudan University,1,73-8.13 Hu Hesheng(1974)J.Fudan University,2,92-8.14 Müller zum Hagen,H.,Seifert,H.J.,and Yodzis,P.(1973)Comm.Math.Phys.,34,134-48).15 Christodoulou,D.(1984)Commun.Math.Phys.,93,171-95.16 Newman,R.(1986)Class.Quantum Grav.,3,527-39.