Numerical investigations of nonlinear behavior in the Einstein equations
The complexity of the Einstein equations of General Relatively poses great challenges to investigator who want to explore and understand the nature of the basis nonlinear physics of the gravitational field. To address this problem, a numerical code is developed as a tool to investigate fully nonlinear behavior in the simplified 1-dimensional vacuum cosmology. In particular, the initial value construction and evolution of linear and nonlinear plane symmetric gravitational waves are studied in an expanding universe described by the Gowdy T{sup 3} class of metrics. A perturbative treatment of the Einstein equations is carried out to obtain analytic descriptions of the gravitational field in both the linear and weakly nonlinear second order regimes. In so doing, conditions are derived necessary for the linearization stability of these solutions. It is demonstrated that the fully nonlinear equations can be solved by testing the code against exact and perturbative analytic solutions. The 3 + 1 split of spacetime and the York formalism are used to decompose the metric and momentum variables into their freely specifiable and constrained pieces. Linear and nonlinear solutions are presented for free data in the form of standing waves and localized packets or pulses. In studying traveling waves pulses, no evidence was found of nonlinear wave propagation. To lowest perturbative order, pulses travel linearly along null rays without dispersing. To second order, these waves interact with the background spacetime inducing a second harmonic oscillation into the background and increasing its expansion rate.
- Research Organization:
- Drexel Univ., Philadelphia, PA (USA)
- OSTI ID:
- 6863067
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
GENERAL RELATIVITY THEORY
EINSTEIN FIELD EQUATIONS
GRAVITATIONAL FIELDS
NONLINEAR PROBLEMS
COSMOLOGY
GRAVITATIONAL WAVES
METRICS
NUMERICAL SOLUTION
PERTURBATION THEORY
SPACE-TIME
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
640106* - Astrophysics & Cosmology- Cosmology
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics