Covariant Hamiltonian boundary term: Reference and quasi-local quantities

The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the quasi-local quantities: energy-momentum, angular-momentum and center-of-mass. The boundary term depends not only on the dynamical variables but also on their reference values; the latter determine the ground state (having vanishing quasi-local quantities). For our preferred boundary term for Einstein's GR we propose 4D isometric matching and extremizing the energy to determine the reference metric and connection values.Comment: 6 pages, contribution to the Proceedings of the Second LeCosPA Symposium "Everything about Gravity", Taipei, 14-18 Dec., 201

Quasi-local energy for cosmological models

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present the quasi-local energy values resulting from the formalism applied to homogeneous Bianchi cosmologies. Finally we consider the quasi-local energies of the FRW cosmologies. Our results do not agree with certain widely accepted quasi-local criteria.Comment: Contributed to International Symposium on Cosmology and Particle Astrophysics (CosPA 2006), Taipei, Taiwan, 15-17 Nov 200

9,10-Dihydro-7H-benzo[de]imidazo[2,1-a]isoquinolin-7-one

In the title compound, C14H10N2O, all non-H atoms are essentially coplanar (r.m.s. deviation = 0.013 Å). The crystal structure is stabilized by π–π stacking inter­actions [centroid–centroid distance = 3.506 (3) Å]