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Alba, David; Lusanna, Luca

Dust in the York canonical basis of ADM tetrad gravity: the problem of vorticity. (English) Zbl 1331.83005

Int. J. Geom. Methods Mod. Phys. 12, No. 7, Article ID 1550076, 52 p. (2015).
Summary: Brown’s formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust, we get the Hamiltonian description in closed form in the York canonical basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally, the Hamiltonian Post-Minkowskian linearization is studied. This formalism is required when one wants to study the Hamiltonian version of cosmological models (for instance back-reaction as an alternative to dark energy) in the York canonical basis.

Cited in 3 Documents

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C40 Gravitational energy and conservation laws; groups of motions
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
53Z05 Applications of differential geometry to physics
83C10 Equations of motion in general relativity and gravitational theory
70H05 Hamilton’s equations
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83A05 Special relativity

Keywords:

general relativity; fluids; York canonical basis; ADM tetrad gravity; perfect fluids; Minkowski space-time; globally hyperbolic, asymptotically Minkowskian space-times; Hamilton equations; clock synchronization gauge freedom; linearization
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References:

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