Mathematics – Mathematical Physics
Scientific paper
Aug 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006tmpg.conf..325m&link_type=abstract
Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebański. Proceedings of 2002 International
Mathematics
Mathematical Physics
Scientific paper
Diffeomorphism covariant theories with dynamical background metric, like gravity coupled to matter fields in the way expressed by Einstein-Hilbert's action or relativistic strings described by Polyakov's action, have `on-shell' vanishing energy-momentum tensor tμν because tμν is, essentially, the Eulerian derivative associated with the dynamical background metric and thus tμν vanishes `on-shell.' Therefore, the equations of motion for the dynamical background metric play a double role: as equations of motion themselves and as a reflection of the fact that tμν = 0. Alternatively, the vanishing property of tμν can be seen as a reflection of the so-called `problem of time' present in diffeomorphism covariant theories in the sense that tμν are written as linear combinations of first class constraints only.
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