New theoretical techniques in the study of gravity

Journal Article · Mon Jan 01 04:00:00 EST 1973 · Gen. Relativity Gravitation, v. 4, no. 4, pp. 309-317

DOI:https://doi.org/10.1007/BF00759850· OSTI ID:4375228

Fischer, A E; Marsden, J E

Using new methods based on first order techniques, it is shown how sharp theorems for existence, uniqueness, and continuous dependence on the Cauchy data for the exterior Einstein equations can be proved simply and directly. The main tools are obtained from the theory of quasi-linear first order symmetric hyperbolic systems of partial differential equations. Einstein's equations in harmonic coordinates are cast into this form, thus achieving a certain uniformity of the description of gravity with other systems of partial differential equations occurring frequently in mathematical physics. In this symmetric hyperbolic form, the Cauchy problem for the exterior equations is easily resolved. Similarly, using first order techniques, a uniqueness theorem can be proved which increases by one the degree of differentiability of the coordinatetransformation between two solutions of Einstein's equations with the same Cauchy data. Finally it is shown how the theory of first order symmetric hyperbolic systems admits a global intrinsic treatment on manifolds. (auth)

• Research Organization: Univ. of California, Santa Cruz
• NSA Number: NSA-29-006828
• OSTI ID: 4375228
• Journal Information: Gen. Relativity Gravitation, v. 4, no. 4, pp. 309-317, Journal Name: Gen. Relativity Gravitation, v. 4, no. 4, pp. 309-317; ISSN GRGVA
• Country of Publication: United Kingdom
• Language: English

Related Subjects

*GRAVITATION-- EINSTEIN FIELD EQUATIONS
COORDINATES
DIFFERENTIAL EQUATIONS
N76300* --Physics (Theoretical)--Gravitation & General Relativity
SYMMETRY