General relativistic continuum mechanics and the post-Newtonian equations of motion

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1991

OSTI ID:5373213

Morrill, T H

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law.

• Research Organization: Boston Univ., MA (United States)
• OSTI ID: 5373213
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONSERVATION LAWS
DATA
DIFFERENTIAL EQUATIONS
DISTRIBUTION
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
INFORMATION
LAGRANGIAN FUNCTION
MASS DISTRIBUTION
MECHANICS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVITY THEORY
SPACE-TIME
SPATIAL DISTRIBUTION
THEORETICAL DATA