SOME FLUID SPHERES AND FLUID PLATES IN GENERAL RELATIVITY

Abstract

Eddington (1924) has pointed out the 4-dimensional space-time manifold of general relativity can be represented as a surface of 4-dimensions drawn in a pseudo-Euclidean flat space of sufficient number of dimensions. It is well known (Eisenhart, 1966) that a 4-dimensinal space-time can be locally and isometrically embedded in a flat space of ten dimensions. The postulates of general relativity don't provide any physical meaning to higher dimensional embedding space. Therefore the purpose of representation of 4-fold as hypersurface is to picture more vividly the metrical properties of the space-time. There are attempts to link the group of motions of flat embedding space to the internal symmetries of elementary particle physics. Some have utilized the higher dimensions to study the singularity of the space-time. In connection of Sakharov's work (1967), the concept of bending of space-time in gravitational theories is dealt by considering space-time embedded in a higher-dimensional space (Regge and Teitelboim, 1975; Maia and Tapia, 1989). Recently the idea that our universe is a 3-brane moving in a higher dimensional space has been revived..