# Accession Number:

## AD0628330

# Title:

## THE NULL BUNDLE OF AN EINSTEIN-RIEMANN SPACE I: GENERAL THEORY,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1966-02-01

# Pagination or Media Count:

## 31.0

# Abstract:

This memorandum examines the structure of all hyperbolic-normal, 4-dimensional metric spaces whose metric tensor can be written in the form h sub AB g sub AB l sub A l sub B where g sub AB is a metric tensor of a given hyperbolic-normal metric space E and l sub A is a null vector in E. The set of all such spaces is termed the null bundle of the space E. Necessary and sufficient conditions are given for selecting elements of the null bundle of E that have the same Ricci tensor andor the same Einstein tensor. In contrast to the general element of the null bundle, these elements are shown to be defined in terms of systems of partial differential equations that are homogeneous in the unknowns. It thus follows that all such elements of the null-bundle are continuously connected to the space E and lie along rays through E in the natural parameterization of the null bundle. These results provide the natural generalization of the results of Kerr and Schild to the cases for which the space E is intrinsically curved and for which the momentum-energy tensor does not vanish. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics
- Quantum Theory and Relativity