Using Eq. (28), we can now rewrite V $^{′′}$( a ) as follows: At the static solution a = a$_{0}$ , the conditions V ( a$_{0}$ ) = 0 and V $^{′}$( a$_{0}$ ) = 0 are indeed met. Now consider the stability criterion V $^{′′}$( a$_{0}$ ) > 0 start- ing with Eq. (31): first let V $^{′′}$( a$_{0}$ ) = 0 and solve for β $^{2}$. We then find that the graph of has a single vertical asymptote (Fig. 3.) To the right of the asymptote, also determined graphically. Returning now to the in- equality V $^{′′}$( a$_{0}$ ) > 0, we therefore have at a = a$_{0}$ So to the right of the asymptote, the region of stability is below the graph of Eq. (32), as shown in Fig. 3. To the left of the asymptote, the sense of the inequality in (33) is reversed and we obtain at a = a$_{0}$ So to the left of the asymptote, the region of stability is above the graph. Fig. 3 does indeed show typical regions of stability using somewhat arbitrary values of the various pa- rameters: r$_{0}$ = 1, r$_{−}$ = 2, r$_{+}$ = 3, and n = 1 / 2. As noted above, the region is below the curve on the right and above the curve on the left. The sign change is determined by inequality (33). These results, including the graphs, are similar to those in Refs. [2] and [19] (dealing with Schwarzschild and dilaton thin-shell wormholes, respectively) in the sense that the regions do not correspond to any value in the interval 0 < β 2 ≤ 1. Since β is ordinarily interpreted as the speed of sound, it is highly desirable to obtain a region for which β 2 < 1. This is indeed possible for our wormhole: if we choose r = r$_{−}$ close to r = r$_{+}$ , then we typically get a region of stability for β 2 < 1. For example, in Fig. 4, r$_{0}$ = 1, r$_{−}$ = 2, r$_{+}$ = 2 . 05, and n = 0 . 8. The closer r$_{−}$ is to r$_{+}$ , the more the region of stability extends below β 2 = 1. A new black-hole solution by Sur, et al. , for Einstein- Maxwell scalar fields was inspired by low-energy string theory. This paper discusses a new thin-shell wormhole VII. CONCLUSION FIG. 4: All functions are the same. Some are cut off. See Fig. 3. FIG. 3: Plot for β 2 versus a$_{0}$ . V $^{′′}$( a ) = f $^{′′}$( a ) − 8 π 2 { [ σ ( a ) + 2 p ( a )] 2 +2 σ ( a ) [( 3 2 − h ( a ) h $^{′′}$( a ) [ h $^{′}$( a )] 2 ) σ ( a ) + p ( a ) ] (1 + 2 β $^{2}$) } . (31) β 2 = − 1 2 + f $^{′′}$/ 8 π 2 − ( σ + 2 p ) 2 4 σ [( 3 2 − hh ′′ ( h ′ ) 2 ) σ + p ] (32) 4 σ [( 3 2 − hh ′′ ( h $^{′}$) 2 ) σ + p ] > 0 , (33) β 2 < − 1 2 + f $^{′′}$/ 8 π 2 − ( σ + 2 p ) 2 4 σ [( 3 2 − hh ′′ ( h ′ ) 2 ) σ + p ] . (34) β 2 > − 1 2 + f $^{′′}$/ 8 π 2 − ( σ + 2 p ) 2 4 σ [( 3 2 − hh ′′ ( h ′ ) 2 ) σ + p ] . (35) 2 4 6 8 10 12 14 a$_{0}$ −3 −2 −1 0 1 2 3 2 4 6 8 10 12 14 a$_{0}$ −3 −2 −1 0 1 2 3 5