Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010gras.conf..193n&link_type=abstract
GRAVITATION AND ASTROPHYSICS. Proceedings of the Ninth Asia-Pacific International Conference. Held 29 June-2 July 2009 in Wuhan,
Astronomy and Astrophysics
Astrophysics
Gravitational Energy, Hamiltonian, Pseudotensors, Quasilocal Energy
Scientific paper
Gravity is the unique interaction which is universal and attractive, distinctive properties directly connected with energy. Identifying a good expression which describes the (quasi-)local energy-momentum of gravitating systems is still an outstanding fundamental puzzle. The traditional pseudotensor approach is considered here along with the more modern quasi-local idea. Using a covariant Hamiltonian boundary-term approach clarifies the geometric and physical ambiguities. Certain criteria can be used as theoretical tests of any proposed quasi-local energy-momentum expression, including positivity, the spatial and null asymptotic limit, and the small region limit. The argument for the positive energy requirement is recalled and some positive energy proofs are noted. Positivity in general is a very strong criterion, but it is not so easy to prove or disprove. Positivity in the small vacuum region limit is simpler, and is also a quite strong test. In particular none of the traditional pseudotensors passes this test. Two natural quasi-local expressions and some other contrived ones do satisfy this small region requirement. The natural expressions have a positive energy proof for finite regions. Conversely, circumstances in which it is appropriate for the energy to be negative are noted. Our covariant Hamiltonian boundary term quasi-local gravitational energy-momentum expression requires, on the boundary, a choice of a displacement vector and field reference values. We have proposed obtaining the reference values from an energy-optimized isometric embedding of the 2-boundary into Minkowski space. This gives reasonable results at least for spherically symmetric regions.
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