Einstein's equations are rewritten in terms of a certain torsionless linear connection $\Gamma^{\alpha}_{\beta\mu}$ which differs, in general, from the Levi-Civita metric connection $\gamma^{\alpha}_{\beta\mu}$. The torsionless connection $\Gamma^{\alpha}_{\beta\mu}$ appears in a natural way as the canonical momentum of the gravitational field $g_{\mu\nu}$. Einstein's equations have a simple interpretation in terms of the connection $\Gamma^{\alpha}_{\beta\mu}$. The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.
On the Equivalence of the Relativistic Theories of Gravitation
FERRARIS, Marco;
1982-01-01
Abstract
Einstein's equations are rewritten in terms of a certain torsionless linear connection $\Gamma^{\alpha}_{\beta\mu}$ which differs, in general, from the Levi-Civita metric connection $\gamma^{\alpha}_{\beta\mu}$. The torsionless connection $\Gamma^{\alpha}_{\beta\mu}$ appears in a natural way as the canonical momentum of the gravitational field $g_{\mu\nu}$. Einstein's equations have a simple interpretation in terms of the connection $\Gamma^{\alpha}_{\beta\mu}$. The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.
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