Hamiltonian theory of self-gravitating perfect fluid and a method of effective deparametrization of Einstein's theory of gravitation

Journal Article · Thu Mar 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.1875· OSTI ID:6901800

Kijowski, J ^[1]; Smolski, A ^[2]; Gornicka, A ^[3]

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1. Institute for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warszawa, Poland (PL)
2. Institute of Mathematics, Technical University, Pl. Jednosci Robotniczej 1, 00-661 Warszawa, Poland (PL)
3. Department of Physics, University of Warsaw, Hoza 69, 00-681 Warszawa, Poland (PL)

The Hamiltonian formulation of the theory of a gravitational field interacting with a perfect fluid is considered. There is a natural gauge related to the mechanical and thermodynamical properties of the fluid, which enables us to describe 2 degrees of freedom of the gravitational field and 4 degrees of freedom of the fluid (together with 6 conjugate momenta) by nonconstrained data ({ital g},{ital P}) where {ital g} is a 3-dimensional metric and {ital P} is the corresponding Arnowitt-Deser-Misner momentum. The Hamiltonian of the theory, numerically equal to the entropy of the fluid, generates uniquely the evolution of the data. The Hamiltonian vanishes on the data satisfying the vacuum constraint equations and tends to infinity elsewhere as the amount of the matter tends to zero. In this way the vacuum theory with constraints is obtained as a limiting case of a deep potential well'' theory.

• OSTI ID: 6901800
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMIC GASES
DIFFERENTIAL EQUATIONS
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
FLUIDS
GASES
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
HAMILTONIANS
LAGRANGE EQUATIONS
MATHEMATICAL OPERATORS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
QUANTUM OPERATORS
SPACE-TIME
TENSORS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
VACUUM STATES