Year: 2026
Type: article
Abstract: We present a systematic construction of traversable wormhole spacetimes featuring two symmetric throats within the framework of General Relativity. Our approach employs the embedding formalism by imposing the analytic relation $$r - r_0 = K(z^2 - a)^2$$ r - r 0 = K ( z 2 - a ) 2 between the radial coordinate and the embedding function, which naturally guarantees the flare-out condition at both throats. This ansatz yields a composite shape function b ( r ) consisting of two branches: an asymptotically flat branch ( $$\epsilon = +1$$ ϵ = + 1 ) extending to spatial infinity, and an intermediate tunnel branch ( $$\epsilon = -1$$ ϵ = - 1 ) with restricted domain $$r_0 \le r \le r_0 + Ka^2$$ r 0 ≤ r ≤ r 0 + K a 2 , connecting the two throats positioned at $$z = \pm \sqrt{a}$$ z = ± a with separation $$2\sqrt{a}$$ 2 a . Analysis of the Einstein field equations reveals that the supporting matter violates the weak, null, and dominant energy conditions throughout the spacetime, while the strong energy condition is identically satisfied with $$\rho + p_r + 2p_t = 0$$ ρ + p r + 2 p t = 0 . A critical finding is the direct connection between throat separation and energy density: configurations with $$0< a < 1/(16Kr_0)$$ 0 < a < 1 / ( 16 K r 0 ) admit positive energy density at the throats with phantom-type radial pressure ( $$\omega _r < -1$$ ω r < - 1 ) and dark-energy-like effective behavior ( $$\omega _{\text {eff}} < 0$$ ω
Source: The European Physical Journal C
Authors: Mauricio Cataldo, Antonella Cid, Pedro Labraña
Institution: University of Bío-Bío
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: Universidad del Bío-Bío
OpenAlex ID: W7155215896