Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.

Share this Page URL

Part IV Branches of Mathematics > IV.13 General Relativity and the Einstein Equ... - Pg. 483

IV.13. General Relativity and the Einstein Equations 483 or for worse, however, the structure necessary to for- mulate Poisson's equation has been incorporated into our traditional mathematical notation and school edu- cation. As a result, R 3 , with its Cartesian coordinate system, and notions such as functions, partial deriva- tives, masses, forces, and so on, are familiar to people with a general mathematical background, while the con- ceptual structure of general relativity is much less so, both with respect to its basic physical notions and with respect to the mathematical objects that are needed to model them. However, once one comes to terms with these, the equations turn out to be more natural and, one might even dare say, simpler. Thus, the first task of this article is to explain in more detail the conceptual structure of general relativ- ity. Our aim will be to make it clear what the equations (1) actually denote, and, moreover, why they are in a cer- Further Reading Brezis, H., and F. Browder. 1998. Partial differential equa- tions in the 20th century. Advances in Mathematics 135: 76­144. Constantin, P. 2007. On the Euler equations of incompress- ible fluids. Bulletin of the American Mathematical Society 44:603­21. Evans, L. C. 1998. Partial Differential Equations. Gradu- ate Studies in Mathematics, volume 19. Providence, RI: American Mathematical Society. John, F. 1991. Partial Differential Equations. New York: Springer. Klainerman, S. 2000. PDE as a unified subject. In *GAFA 2000*, Visions in Mathematics--Towards 2000 (special issue of Geometric and Functional Analysis), part 1, pp. 279­315. Wald, R. M. 1984. General Relativity. Chicago, IL: Chicago University Press.