Positive energy density in topologically charged exponential wormholes and Regge–Wheeler potential

Abstract In this paper, we investigate a series of topologically charged exponential traversable wormhole models described by the standard metric form: alignedds²=- A² (r) \, dt²+ B² (r) \, dr² ²+r²\, (d ²+ ² \, d ²), aligned d s 2 = - A 2 (r) d t 2 + B 2 (r) d r 2 α 2 + r 2 (d θ 2 + sin 2 θ d ϕ 2), where 0 0 α 1 is the global monopole chare parameter. We focus on the positivity of the energy density across these models, defined by the following functions: (i) A (r) = (-Mr) A (r) = exp - M r and B (r) = (Mr+ \, r) B (r) = exp M r + β r, (ii) A (r) = (-Mr- \, r) A (r) = exp - M r - γ r and B (r) = (Mr) B (r) = exp M r, and (iii) A (r) = (-Mr- \, r) A (r) <mml: