3 III. CONCLUSION Φ $^{′}$( r ), we get Φ $^{′}$( r ) = 1 2 r ( e 2Λ( r ) − 1 ) + A [ Λ $^{′}$( r ) + 1 2 r ( e 2Λ( r ) − 1 ) ] − (8 π ) 1+ $^{α}$B ( r $_{2}$) e 2Λ( r ) [ 2 $_{r}$e − 2Λ( r $^{)}$Λ ′ ( r ) + 1 r 2 ( 1 − e − 2Λ( r ) )] $_{α}$. (16) We have shown in this note that exact solutions of certain wormhole geometries, such as traversable wormholes sup- ported by phantom energy, Chaplygin and generalized Chaplygin gas, or modified Chaplygin gas, imply the ex- istence of entire families of additional solutions. Having an abundance of solutions is highly desirable since ex- act solutions often have the appearance of being overly specialized or even artificial. Since the left side is well behaved (due to the choice of d ), the right side is also well behaved in the sense of being finite and sectionally continuous. As before, we can replace Λ( r ) by Λ( r ) + ϵ ( r ), where, once again, ϵ = ϵ ( r ) has a continuous derivative with ϵ ( r$_{0}$ ) = ϵ $^{′}$( r$_{0}$ ) = 0 and ϵ ( r ) → 0 as r → ∞ . Now denote the left side by Φ ′ $_{1}$( r ). Since Φ ′ $_{1}$( r ) is also sectionally continuous, Φ$_{1}$( r ) will exist, again showing the existence of an entire family of solutions. From a physical standpoint, the proliferation of solu- tions, given the various equations of state, would greatly increase the probability of wormholes’ having formed nat- urally. In particular, it is argued in Ref. [5] that the EoS had very likely crossed the “phantom divide” some time in the past, so that wormholes could have formed natu- rally. In approaching the present dark-energy phase, such wormholes would have formed event horizons, thereby becoming black holes or (possibly) quasi-black holes. This outcome provides at least a possible explanation for the abundance of black holes and the complete lack of wormholes. Physical Review D, 71 (2005), Article ID 084011, 8 pages. [1] J. Bicak, Einstein equations: exact solutions, arXiv: gr-qc/0604102. [2] S. Chakraborty and T. Bandyopadhyay, Modified Chap- lygin traversable wormholes, International Journal of Modern Physics D, 18 (2007), 463-476. [3] P.K.F. Kuhfittig, Seeking exactly solvable models of traversable wormholes supported by phantom energy, Classical and Quantum Gravity, 23 (2006), 5853-5860. [4] P.K.F. Kuhfittig, Theoretical construction of wormholes supported by Chaplygin gas, arXiv: 0802.3656. [5] P.K.F. Kuhfittig, Could some black holes have evolved from wormholes? Scholarly Research Exchange, 2008 (2008), Article ID 296158, 5 pages. [6] F.S.N. Lobo, Phantom energy traversable wormholes, [7] F.S.N. Lobo, Chaplygin traversable wormholes, Physical Review D, 73 (2006), Article ID 064028, 9 pages. [8] F.S.N. Lobo, Van der Waals quintessence stars, Physical Review D, 75 (2007), Article ID 024023, 7 pages. [9] M.S. Morris and K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teach- ing general relativity, American Journal of Physics, 56 (1988), 395-412. [10] O.B. Zaslavskii, Exactly solvable models of wormholes supported by phantom energy, Physical Review D, 72 (2005), Article ID 061303, 3 pages.