Positivity of energy in five-dimensional classical unified field theories

Details Positivity of energy in five-dimensional classical unified field theories Positivity of energy in five-dimensional classical unified field theories

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985lmaph...9..243t&link_type=abstract

Letters in Mathematical Physics, Volume 9, Issue 3, pp.243-253

Mathematics

Mathematical Physics

4

Scientific paper

Five-dimensional classical unified field theories as well as in Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five-dimensional space V 5 with metric tensor y ;; which admits a space-like Killing vector ξα. It is assumed that: (1) V 5 has the topology of V 4× S 1, S 1 is a circle and V 4 is a four-dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γαβ of V 5 satisfies Γ _{α β } u^α v^β ≤slant 0, where u α and v β are future oriented time-like vectors with γ _{α β } \upsilon ^α ξ ^β = 0. The spinor approach of Witten, Nester, and Moreschi and Sparling is used to show that the conserved five-dimensional energy momentum vector P ; is nonspace-like. If P ;=Γαβ=0 then V 5 must admit a time-like Killing vector. Lichnerowicz's results then imply that V 5 must be flat. A lower bound for P 4 (the mass) similar to that found by Gibbons and Hull is obtained.

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