Spectrum of Wormholes, pp. 2655-2663 in: Physical Review D, Vol. 42, No. 8, 15 October 1990. HAWKING ON WORMHOLES

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First edition, journal issue in original printed wrappers, of the first quantum-mechanical analysis of wormholes. "Wormholes have been studied mainly in the semiclassical approximation as solutions of the classical Euclidean field equations. However, such solutions are rather special, and exist only for certain kinds of matter. On the other hand, one can represent wormholes in a more general manner as solutions of the Wheeler-DeWitt equation with appropriate boundary conditions" (Abstract). The authors find a discrete spectrum of solutions of this equations which suggests (but does not prove) that wormholes may exist in nature. "Stephen questioned not only whether quantum gravity would be predictable, but also whether it would be causal. Suggested culprits were the 'wormholes', possible entities whose potential importance had been emphasized by Wheeler. They can be thought of as short tunnels connecting apparently distant regions of space or space-time. In fact, there are two different types of wormhole. Those considered by Wheeler correspond to three-dimensional spatial sections of an ordinary four-dimensional space-time with non-trivial topology. An immediate question was whether the topology might change dynamically. Using what is called co-bordism theory, Wheeler's student, Robert Geroch, had shown that, although the possibility is allowed, any smooth metric in between two topologically-distinct spatial sections must admit closed time-like curves which would therefore allow time travel. Much later, Thorne argued that the mere existence of a wormhole could allow the construction of a time machine, although it had to be built of exotic material which violates the energy conditions used to establish the singularity theorems. Such violations are possible according to quantum field theory, but Stephen conjectured that the existence of closed time-like curves would lead to quantum field theoretic back reaction effects which prevent the construction of such wormholes in the first place" (Hawking's Royal Society Obituary Notice). 4to, pp. 2437-2966. Original printed wrappers (slight discolouration to a small area at the top and minor crease to lower outer corner of the front wrapper). A very good copy with no stamps or other markings. N° de ref. del artículo ABE-1643131316996

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