Conformal relations and Hamiltonian formulation of fourth-order gravity

Details Conformal relations and Hamiltonian formulation of fourth-order gravity Conformal relations and Hamiltonian formulation of fourth-order gravity

1997-12-29

arxiv.org/abs/gr-qc/9712097v1

Grav.Cosmol. 3 (1997) 266-274

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, LaTeX, no figures, Grav. and Cosmol. to appear February 1998

Scientific paper

The conformal equivalence of fourth-order gravity following from a non-linear Lagrangian L(R) to theories of other types is widely known, here we report on a new conformal equivalence of these theories to theories of the same type but with different Lagrangian. For a quantization of fourth-order theories one needs a Hamiltonian formulation of them. One of the possibilities to do so goes back to Ostrogradski in 1850. Here we present another possibility: A Hamiltonian H different from Ostrogradski's one is discussed for the Lagrangian L depending on first and second order drivatives of the position variable q. We add a suitable divergence to L. Contrary to other approaches no constraint is needed. One of the canonical equations becomes equivalent to the fourth-order Euler-Lagrange equation of L. Finally, we discuss the stability properties of cosmological models within fourth-order gravity.

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