Closed timelike smooth curves in the general theory of relativity (original) (raw)
For a space-time which admits a closed timelike smooth curve it is estimatedthat~" ~2 9 10-24 9 ~p l 2, where 9 is the real time and l the spatial length associated with the timelike curve, and p is the density of material. In connection with Howard's paper [i] dealing with the cosmological model of C~del [2] and particularly with GSdel's statement that a closed timelike smooth curve exists in his model, it is important to reconsider this interesting problem in the general theory of relativity. Howard casts some doubt on the result of Chandrasekhar and Wright [3] that a closed timelike smooth geodesic is impossible in the GSdel model. It is shown below that the original conclusion in [3] is correct. Different opinions have been expressed about models which admit closed timelike smooth curves (timelike eycles)(see [5]; [8]; [6], p. 625. The estimates which we make below, however, show that the phenomena either cannot be observed in practice, or are only realized in areas where modern physics has not yet penetrated, or must be considered from, say, a quantum-mechanical rather than a classical point of view. Let { I i}mi =1 (m >-1), the intervals containing the zeroes of the function f~' (t), be so small that
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