We have investigated the stability of a set of nonrotating anisotropic spherical models with a phasespace distribution function of the Osipkov-Merritt type. The velocity distribution in these models is isotropic near the center and becomes radially anisotropic at large radii. The models are special members of the family studied by Dehnen and by Tremaine et al. in which the mass density has a power-law cusp o P r~c at small radii and decays as o P r~4 at large radii.The radial-orbit instability of models with c \ 0, 1/2, 1, 3/2, and 2 was studied using an N-body code written by one of us and based on the "" self-consistent Ðeld ÏÏ method developed by Hernquist & Ostriker. These simulations have allowed us to delineate a boundary in the (c, that separates r a )-plane the stable from the unstable models. This boundary is given by for the ratio of the 2T r /T t \ 2.31^0.27 total radial to tangential kinetic energy. We also found that the stability criterion df/dQ ¹ 0, recently raised by Hjorth, gives lower values compared with our numerical results.The stability to radial modes of some Osipkov-Merritt c-models that fail to satisfy the Doremus-Feix criterion Lf/LE \ 0 has been studied using the same N-body code but retaining only the l \ 0 terms in the potential expansion. We have found no signs of radial instabilities for these models.
We study a solution of Einstein's equations that describes a straight cosmic string with a variable angular deficit, starting with a 2 π deficit at the core. We show that the coordinate singularity associated to this defect can be interpreted as a traversible wormhole lodging at the the core of the string. A negative energy density gradually decreases the angular deficit as the distance from the core increases, ending, at radial infinity, in a Minkowski spacetime. The negative energy density can be confined to a small transversal section of the string by gluing to it an exterior Gott's like solution, that freezes the angular deficit existing at the matching border. The equation of state of the string is such that any massive particle may stay at rest anywhere in this spacetime. In this sense this is 2+1 spacetime solution.A generalization, that includes the existence of two interacting parallel wormholes is displayed. These wormholes are not traversible.Finally, we point out that a similar result, flat at infinity and with a 2 π defect (or excess) at the core, has been recently published by Dyer and Marleau. Even though theirs is a local string fully coupled to gravity, our toy model captures important aspects of this solution.
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