Hamiltonian formalism for perfect fluids in general relativity

Journal Article · Thu May 15 00:00:00 EDT 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.2785· OSTI ID:5445979

Demaret, J; Moncrief, V

Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = ..gamma.. < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models.

• Research Organization: Institut d'Astrophysique, Universite de Liege, B 4200 Cointe-Ougree, Belgium
• OSTI ID: 5445979
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640106 -- Astrophysics &amp; Cosmology-- Cosmology
657003* -- Theoretical &amp; Mathematical Physics-- Relativity &amp; Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BARYON NUMBER
COSMOLOGICAL MODELS
FIELD THEORIES
FLUID MECHANICS
FLUIDS
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HAMILTONIANS
HYDRODYNAMICS
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM OPERATORS
SPACE-TIME
UNIVERSE