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 2π. 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.

Energy theorem for (2+1)-dimensional gravity / P. MENOTTI; D. SEMINARA. - In: ANNALS OF PHYSICS. - ISSN 0003-4916. - STAMPA. - 240(1995), pp. 203-221. [10.1006/aphy.1995.1044]

Energy theorem for (2+1)-dimensional gravity

SEMINARA, DOMENICO
1995

Abstract

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 2π. 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.
240
203
221
P. MENOTTI; D. SEMINARA
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/223009
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