Studies in higher-derivative gravitation
In this work two formulations of gravitation in which the action includes the second-derivatives of the metric in a non-trivial fashion are investigated. In the first part, the gauge theory of gravitation proposed by Yang in 1974 is investigated. The implications of coupling the pure space equations to matter sources via the action principle proposed by Yang is studied. It is shown that this action principle does not couple to matter sources in a satisfactory fashion. An earlier study by Fairchild along similar lines is critically examined. It is argued that Fairchild's action functional, and his objections to Yang's gauge approach to gravitation, arise from a not very meaningful analogy with the case of a general gauge field. Also, a conjecture originated in that work is refuted. A modification of Yang's action functional is provided which leads to both the Einstein and Yang field-equations. This system is shown to have non-trivial solutions in the presence of matter. An additional advantage is that the unphysical solutions of the pure space equations can be ruled out. It is shown that the joint system of Einstein and Yang field-equations leads to a physically viable cosmological model based on the Robertson-Walker metric, which satisfies both sets of field-equations. In the second part of this work, the Hamiltonian for pure gravity in Einstein's theory is obtained directly from the Hilbert Lagrangian. Since the Lagrangian depends upon the second-derivatives of the metric tensor, first the Hamiltonian formulation for a Lagrangian which may, in general depend upon the Nth-order time derivatives of the dynamical variables is developed.
- Research Organization:
- State Univ. of New York, Stony Brook, NY (USA)
- OSTI ID:
- 5537881
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
GRAVITATION
FIELD THEORIES
COMPARATIVE EVALUATIONS
COSMOLOGICAL MODELS
DIRAC EQUATION
EINSTEIN FIELD EQUATIONS
FIELD EQUATIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
HAMILTONIANS
LAGRANGIAN FUNCTION
MATTER
METRICS
MODIFICATIONS
YANG-MILLS THEORY
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
WAVE EQUATIONS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation