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Weekly Report

Weekly Report. 100208 Yu- Chiao Chang. Non-relativistic gravity. A.A. Kocharyan’s paper: “ I s non-relativistic gravity possible? ” Superspace :

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Weekly Report

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  1. Weekly Report 100208 Yu-Chiao Chang

  2. Non-relativistic gravity • A.A. Kocharyan’s paper: “Is non-relativistic gravity possible? ” • Superspace: • Let M be an oriented without boundary manifold. Let be the space of all symmetric two tensors on M and let be the manifold of positive definite Riemannian metrics on M.

  3. The tangent bundle of is . • Let be the space of all symmetric two contravariant tensor densities on M. The cotangent bundle of is • We have a natural pairing between given by:

  4. The DeWitt metric on is given by • The metric G has an inverse metric given by

  5. Hamiltonian formulation • We investigate a dynamical system on given by an invariant action: • Note thatthis Kocharyan considers N is time dependent only, different from Miao Li’s condition, this may result in different conclusion!

  6. The canonical momenta conjugate to are • and the Hamiltonian is

  7. Hamiltonian equations have the following form:

  8. Following the setup, we will consider the constraint structure and comparing with Miao Li’s argument! • Motivation of studying this paper is to find possible ways to rewrite Cook’s theory in ADM formalism, at least some hints. • This paper takes a more mathematical point of view to the non-relativistic gravity, higher than Horava’s theory, so if we want to develop non-relativistic gravity, I think we should pay some attention to this one.

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