# The double role of Einstein's equations: as equations of motion and as vanishing energy-momentum tensor

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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## Details The double role of Einstein's equations: as equations of motion and as vanishing energy-momentum tensor The double role of Einstein's equations: as equations of motion and as vanishing energy-momentum tensor

7 pages, no figures, latex file. Contribution to the meeting in honor of Plebanski. Any comments on this issue are welcome

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 $t_{\mu\nu}$ because $t_{\mu\nu}$ is, essentially, the Eulerian derivative associated with the dynamical background metric and thus $t_{\mu\nu}$ 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 $t_{\mu\nu}=0$. Alternatively, the vanishing property of $t_{\mu\nu}$ can be seen as a reflection of the so-called `problem of time' present in diffeomorphism covariant theories in the sense that $t_{\mu\nu}$ are written as linear combinations of first class constraints only.

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