Einstein geometry and hyperbolic equations.(English)Zbl 0659.35087

Directions in partial differential equations, Proc. Symp., Madison/Wis. 1985, Publ. Math. Res. Cent. Univ. Wis. Madison 54, 113-143 (1987).
[For the entire collection see Zbl 0643.00011.]
The aim of this lecture is to discuss the relation between the geometry of the Minkowski space, generalized energy estimates and uniform rates of decay for two other examples of linear field equations in Minkowski space: (M) Maxwell equations; (Sp) Spin-2 field equations. For completeness we also consider ($$\square)$$ Scalar wave equation.
Our main interest is the study of (Sp) and its connection to an outstanding problem in general relativity which we state below. All the results presented in this lecture were derived in collaboration with D. Christodoulou [Einstein geometry and linear field equations in Minkowski space (in preparation)].

MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 35A30 Geometric theory, characteristics, transformations in context of PDEs 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)

Zbl 0643.00011