A ug 1 99 9 Gravitational memory of natural wormholes

A traversable wormhole solution of general scalar–tensor field equations is presented. We have shown, after a numerical analysis for the behavior of the scalar field of Brans-Dicke theory, that the solution is completely singularity– free. Furthermore, the analysis of more general scalar field dependent coupling constants indicates that the gravitational memory phenomenon may play an important role in the fate of natural wormholes. 1 Notwithstanding various possible exceptions, the mandate of the energy conditions (encoded in the evolution of the expansion scalar governed by Raychaudhuri's equation) is a popular tenet of belief in any current research field [1]. The simplest possible stellar environment that militate against these conjectures is usually called a " wormhole throat " [2]. Wormhole physics dates back at least as far as 1916 [3], with punctuated revivals of activity following both the classical work of Einstein–Rosen [4] and the seminal paper by Wheeler [5], but, the concept of traversable wormhole was not put forward until 1988 with the work by Morris–Thorne (MT) [6]. Nowadays, the broad phylum of wormholes can be precisely defined in terms of null geodesic congruences propagating outward from, and orthogonal to, an extremal hypersurface of minimal area known as the wormhole throat [7]. Unlike MT's embedding approach, this new characterization (that accurately captures the essence of the local physics which operates near any wormhole throat) is free from assumptions about symmetries, asymptotic flattness, embedded diagrams and even time dependence. We hasten to point out however, that throughout this article we shall use the word " wormhole " to specify the sub-class of traversable entities introduced by MT [6], namely, a compact S 2 tunnel connecting two asymptotically flat spacetimes. In order to expand such a configuration along the radial direction, the derivative of the S 2 radius with respect to the proper coordinate l must be positive near the throat. Since this derivative is proportional to the energy momentum tensor on the radially directed null geodesic, a large inward pressure is required on the tunnel to sustain the wormhole structure, yielding a violation of the null energy condition. Very recently the consequences of the energy conditions were confronted with possible values of the Hubble parameter and the gravitational redshifts of the oldest stars in the galactic halo [8]. It was deduced that for the currently favored values of H 0 , the strong energy condition should have been violated sometime between the …