Research Articles

General Relativity and Gravitation

, Volume 7, Issue 12, pp 915-920

First online:

A new Hamiltonian structure for the dynamics of general relativity

  • Arthur E. FischerAffiliated withDepartment of Mathematics, University of California
  • , Jerrold E. MarsdenAffiliated withDepartment of Mathematics, University of California

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A new compact form of the dynamical equations of relativity is proposed. The new form clarifies the covariance of the equations under coordinate transformations of the space-time. On a deeper level, we obtain new insight into the infinite-dimensional symplectic geometry behind the dynamical equations, the decompositions of gravitational perturbations, and the space of gravitational degrees of freedom. Prospects for these results in studying fields coupled to gravity and the quantization of gravity are outlined.