5,403 research outputs found
General Volume-Preserving Mechanical Systems
In this letter, we present the general form of equations that generate a
volume-preserving flow on a symplectic manifold (M, \omega). It is shown that
every volume-preserving flow has some 2-forms acting the role of the
Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton
equations are included as a special case with a 2-form \frac{1}{n-1} H \omega
where H is the corresponding Hamiltonian.Comment: Plain LaTeX, 13 pages, no figure
Temperature at Horizon in de Sitter Spacetime
It is found that there is no period in the imaginary Beltrami-time of the de
Sitter spacetime with Beltrami metric and that the `surface-gravity' in view of
inertial observers in de Sitter spacetime is zero! They show that the horizon
might be at zero temperature in de Sitter spacetime and that the thermal
property of the horizon in the de Sitter spacetime with a static metric should
be analogous to that of the Rindler horizon in Minkowski spacetime.Comment: 7 pages, 1 figur
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