GENERALIZED RIEMANN SPACES AND GENERAL RELATIVITY. II

Generalized Riemann Spaces and General Relativity.

spectrum of K, and fixed t > 0. As a consequence, u(-, t) lies in the range of (K tI), and by Theorem 3 of Paper I, after a replacement on a set of measure zero, u(-, t) lies in C"T(D). If Eg(x) is the smooth representative of its equivalence class in L2' r(D), for any Borel set A in El lying in the interval XI < a, by Theorem 3 of Paper I, IE(A)g(x)I = I(K, I)-j(K R I)jE(A)g(x)I < C(oaI + I I)...

Semi-Riemann Geometry and General Relativity

Pointless Spaces in General Relativity

The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise to points by loosing a part of the entire structure is discussed. The counterpart of the traditional objects of differential geometry are studied. FOREWORD In...

Part II General Relativity

1 Part II: Introduction General Relativity (16 lectures) 2 1.1 Pre-requisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Signature Convention . . . . . . . . . . . . . . . . . . . . . . . . 2 1.5 Curvature Conventions ....

General relativity histories theory II : Invariance groups

In this paper we show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphisms group and the Dirac algebra of constraints. We show that the introduction of metric-dependent equivariant foliations leads to the crucial result that the canonical constraints are invariant under the action of spacetime diffeomorphisms. Furthermore, t...