B. Near core expansion We can Taylor expand the equations of motion about the tip of the cigar. This leaves two unknown boundary conditions, which we will use as shooting parameters. For n = 1 they are ℓ and f ′ $_{0}$. The remaining terms are then completely specified: which give the solution where the numerical solution was matched to the background in a box of circumference 25 . 566 H − $^{1}$. Our chosen parameter values are rather generic, but we expect a large range of solutions to exist. In particular, we can smoothly deform our parameters and corresponding solution to match the bubble of Witten. This is shown in the solution Fig. (5), where the chosen parameters are which give the solution B ( r ) = ℓ +$^{(}$ 1 2 ℓ − κ $^{2}$ℓ ( η $^{4}$λ + 4Λ) 24 ) r 2 + ... (36) C ( r ) = 1 +$^{(}$ − 1 2 ℓ 2 + κ 2 $^{(}$η $^{4}$λ + 4Λ − 12 f ′ 0 2 ) 72 ) r 2 + ... (37) f ( r ) = f ′ $_{0}$r + ... (38) We then numerically integrate the equations of motion outward from r = 0 to obtain the functions pictured in Fig. (4). The numerical values for the parameters used are n = 1 Λ = − (0 . 347 M$_{P}$ ) 5 η = (0 . 630 M$_{P}$ ) 3 / 2 λ = (0 . 995 M$_{P}$ ) − 1 , (39) H = 0 . 0332 M$_{P}$ L = (0 . 118 M$_{P}$ ) − 1 ℓ = (0 . 0806 M$_{P}$ ) − 1 f ′ 0 = (0 . 456 M$_{P}$ ) 5 / 2 , (40) S$_{B}$ = S$_{E}$ [bubble] − S$_{E}$ [compactification] ≈ 7 . 4 × 10 4 , (41) n = 1 Λ = − (0 . 224 M$_{P}$ ) 5 η = (0 . 422 M$_{P}$ ) 3 / 2 λ = (4 . 50 M$_{P}$ ) − 1 , (42) H = 0 . 010 M$_{P}$ L = (0 . 100 M$_{P}$ ) − 1 ℓ = (0 . 0985 M$_{P}$ ) − 1 f ′ 0 = (0 . 179 M$_{P}$ ) 5 / 2 . (43) where M$_{P}$ = κ − 2 / 3 is the 5 d reduced Planck mass. The Euclidean action of this solution is given by 10