Compactified vacuum in ten dimensions

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:5096920

Wurmser, D

Since the 1920's, theories which unify gravity with the other fundamental forces have called for more than the four observed dimensions of space-time. According to such a theory, the vacuum consists of flat four-dimensional space-time described by the Minkowski metric M{sup 4} and a compactified space B. The dimensions of B are small, and the space can only be observed at distance scales smaller than the present experimental limit. These theories have had serious difficulties. The equations of gravity severely restrict the possible choices for the space B. The allowed spaces are complicated and difficult to study. The vacuum is furthermore unstable in the sense that a small perturbation causes the compactified dimensions to expand indefinitely. There is an addition a semi-classical argument which implies that the compactified vacuum by annihilated by virtual black holes. It follows that a universe with compactified extra dimensions could not have survived to the present. These results were derived by applying the equations of general relativity to spaces of more than four dimensions. The form of these equations was assumed to be unchanged by an increase in the number of dimensions. The authors illustrate the effect of such terms by considering the example B = S{sup 6} where S{sup 6} is the six-dimensional sphere. Only when the extra terms are included is this choice of the compactified space allowed. He explore the effect of a small perturbation on such a vacuum. The ten-dimensional spherically symmetric potential is examined, and I determine conditions under which the formation of virtual black holes is forbidden. The examples M{sup 4} {times} S{sup 6} is still plagued by the semi-classical instability, but this result does not hold in general. The requirement that virtual black holes be forbidden provides a test for any theory which predicts a compactified vacuum.

• Research Organization: Johns Hopkins Univ., Baltimore, MD (USA)
• OSTI ID: 5096920
• Country of Publication: United States
• Language: English

Related Subjects

640100* -- Astrophysics & Cosmology
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
COMPACTIFICATION
FIELD THEORIES
GRAVITATIONAL FIELDS
GRAVITATIONAL INSTABILITY
INSTABILITY
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL MODELS
PLASMA INSTABILITY