islands develop or not. Since the hopes for obtaining thin-shell wormholes with normal matter when α > 0 , have already been dashed [5], we shall investigate here only the case for α < 0 . In order to analyze the behavior of V ( a ) (and its second derivative) we introduce new parameterization as follows Accordingly, our new variables f (˜ a ) , ˜ σ 0 , ˜ p 0 , A and B take the following forms and Following this parametrization our Eq. (25) takes the form where In the next section we explore all possible constraints on our parameters that must satisfy to materialize a stable, normal matter wormhole through the requirement V $^{′′}$(˜ a ) > 0 . 7 IV. CONSTRAINTS VERSUS FINELY-TUNED PARAMETERS AND SECOND DERIVATIVE PLOTS OF THE POTENTIAL ˜ a 2 = − a 2 α , m = − 16 M πα , q 2 = 8 Q 2 3 α 2 , ˜ σ 0 = √ − ασ 0 , p 0 = √ − αp 0 (29) f (˜ a ) = 1 − ˜ a 2 4 + ˜ a 2 4 √ 1 − m ˜ a 4 + q 2 ˜ a 6 (30) ˜ σ 0 = − √ f (˜ a 0 ) 4 π [ 3 ˜ a 0 + 4 ˜ a 3 0 ( f (˜ a 0 ) − 3) ] , (31) ˜ p 0 = f (˜ a 0 ) 4 π [ 2 ˜ a 0 + f $^{′}$(˜ a 0 ) 2 f (˜ a 0 ) + 2 ˜ a 2 0 f $^{′}$(˜ a 0 ) f (˜ a 0 ) ( f (˜ a 0 ) − 1) ] , (32) A = − π ˜ a 3 4 [ ( ˜ σ 0+ ˜ p 0 β 2 + 1 ) ( ˜ a 0 ˜ a ) 3 ( β $^{2}$+1 ) + β $^{2}$˜ σ 0 $_{−}$˜ p 0 β 2 + 1 ] , (33) B = − ˜ a 2 8 + 1 − f (˜ a ) 2 . (34) ( d ˜ a dτ ) 2 + ˜ V (˜ a ) = 0 , (35) ˜ V (˜ a ) = − V (˜ a ) α . (36) i ) Starting from the metric function we must have