Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1994-06-08
Annals Phys. 240 (1995) 203-221
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
(Revtex), 24 pages,MIT-CTP#2324 snd IFUP-TH-33/94
Scientific paper
10.1006/aphy.1995.1044
We prove a positive energy theorem in 2+1 dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson loops and show that the energy-momentum of the enclosed subsystem is a future directed time-like vector whose mass is an increasing function of the loop, until it reaches the value $1/4G$ corresponding to a deficit angle of $2\pi$. At this point the energy-momentum of the system evolves, depending on the nature of a zero norm vector appearing in the evolution equations, either into a time-like vector of a universe which closes kinematically or into a Gott-like universe whose energy momentum vector, as first recognized by Deser, Jackiw and 't Hooft is space-like. This treatment generalizes results obtained by Carroll, Fahri, Guth and Olum for a system of point-like spinless particle, to the most general form of matter whose energy-momentum tensor satisfies the dominant energy condition. The treatment is also given for the anti de Sitter 2+1 dimensional gravity.
Menotti Pietro
Seminara Domenico
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