Partial Differential Equations of Physics

Details Partial Differential Equations of Physics Partial Differential Equations of Physics

1996-02-27

arxiv.org/abs/gr-qc/9602055v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

57 pages Latex, 0 figures

Scientific paper

Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of differential equations so formulated. Examples of such features include hyperbolicity of the equations, constraints and their roles (e.g., in connection with the initial-value formulation), how diffeomorphism freedom is manifest, and how interactions between systems arise and operate. Second, we give a number of examples that illustrate how the equations for physical systems are cast into this form. These examples suggest that the first-order, quasilinear form for a system is often not only the simplest mathematically, but also the most transparent physically.

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