On the Status of Wormholes in Einstein’s Theory: An Overview

  • Peter K.F. Kuhfittig Department of Mathematics, Milwaukee School of Engineering, Milwaukee, Wisconsin 53202-3109, USA
Keywords: traversable wormholes, higher dimensions, noncommutative geometry, emergence, neutron stars, fine-tuning, Casimir effect


It has been claimed that wormholes are just as good a prediction of Einstein’s theory as black holes, but
they are subject to severe restrictions from quantum field theory. The purpose of this paper is to show that
the claim can be substantiated in spite of these restrictions.


Note to editor: The emphasis in this paper is on problems that are usually ignored. For example, the need for exotic matter is considered to be completely unphysical by many researchers. This paper also includes a new finding, which is that neither dark matter nor non-phantom dark energy can by themselves support traversable wormholes. The goal is to show that traversable wormholes can in principle exist without requiring a modification of Einstein's theory, the usual alternative. This is accomplished by hypothesizing an extra spatial dimension, either static or time dependent, by appealing to an emergent phenomenon, noncommutative geometry, which, like extra spatial dimensions, is consistent with string theory. Another possibility is the careful fine-tuning of the metric coefficients, thereby permitting small violations of the null energy condition, as exemplified by the Casimir effect, also discussed in the paper. Finally, the enormous radial tension at the throat suggests that moderately-sized wormholes are actually compact stellar objects such as neutron stars.
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