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

Abstract

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.

Authors:
 [1];  [2];  [3]
  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)
Publication Date:
OSTI Identifier:
6901800
Resource Type:
Journal Article
Journal Name:
Physical Review, D (Particles Fields); (USA)
Additional Journal Information:
Journal Volume: 41:6; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMIC GASES; GRAVITATIONAL FIELDS; GENERAL RELATIVITY THEORY; HAMILTONIANS; EINSTEIN FIELD EQUATIONS; ENERGY-MOMENTUM TENSOR; LAGRANGE EQUATIONS; METRICS; SPACE-TIME; THERMODYNAMIC PROPERTIES; THREE-DIMENSIONAL CALCULATIONS; VACUUM STATES; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; FLUIDS; GASES; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES; QUANTUM OPERATORS; TENSORS; 645400* - High Energy Physics- Field Theory; 657003 - Theoretical & Mathematical Physics- Relativity & Gravitation

Citation Formats

Kijowski, J, Smolski, A, and Gornicka, A. Hamiltonian theory of self-gravitating perfect fluid and a method of effective deparametrization of Einstein's theory of gravitation. United States: N. p., 1990. Web. doi:10.1103/PhysRevD.41.1875.
Kijowski, J, Smolski, A, & Gornicka, A. Hamiltonian theory of self-gravitating perfect fluid and a method of effective deparametrization of Einstein's theory of gravitation. United States. https://doi.org/10.1103/PhysRevD.41.1875
Kijowski, J, Smolski, A, and Gornicka, A. 1990. "Hamiltonian theory of self-gravitating perfect fluid and a method of effective deparametrization of Einstein's theory of gravitation". United States. https://doi.org/10.1103/PhysRevD.41.1875.
@article{osti_6901800,
title = {Hamiltonian theory of self-gravitating perfect fluid and a method of effective deparametrization of Einstein's theory of gravitation},
author = {Kijowski, J and Smolski, A and Gornicka, A},
abstractNote = {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.},
doi = {10.1103/PhysRevD.41.1875},
url = {https://www.osti.gov/biblio/6901800}, journal = {Physical Review, D (Particles Fields); (USA)},
issn = {0556-2821},
number = ,
volume = 41:6,
place = {United States},
year = {Thu Mar 15 00:00:00 EST 1990},
month = {Thu Mar 15 00:00:00 EST 1990}
}