The key point is to the physical laws that react on a traversible wormhole solution i.e if we use all knowledge about classical mechanics, is it then possible that a traversible wormhole can exist? The wormhole metric can be describe by this metric.
ds^2 = -e^{2\Phi}dt^2 + d\rho^2 + r^2(d\theta^2 + \sin^2 \theta d\phi^2)
The strategy is to find the components of the Einstein tensor and to find the three differential equations, where each one respectively describes the mass-energy, radial tension and the lateral pressure as a function of the radial coordinate, and by use of these make a statement about the future and the maintenance of the wormhole.
The expansion of the geodadic by covariant point separations metods is,
T^{\mu \nu}(x, x^{\prime}) = \lim_{x \rightarrow x^{\prime}}\left[ g^{\mu \lambda}(x)g^{\nu^{\prime} \omega^{\prime}}(x^{\prime}) - \frac{1}{4} g^{\mu \nu^{\prime}}(x^{\prime})g^{\lambda \omega^{\prime}}(x^{\prime})\right]\cdot \newline \frac{1}{2}g^{\rho \tau^{\prime}}(x^{\prime})\left( F_{\lambda \rho}(x)\tilde{F}_{\omega \tau}(x^{\prime}) + \tilde{F}_{\lambda \rho}(x^{\prime})F_{\omega \tau}(x) \right)and
\lim_{\rho \rightarrow \rho^{\prime}}g_{\mu \nu^{\prime}}{ ;}{\tau} = \lim_{\rho \rightarrow \rho^{\prime}}g_{\lambda \nu^{\prime}}\hspace{2pt} g^{\lambda \rho}\frac{1}{2}(\partial_{\tau}g_{\mu \rho} + \partial_{\mu}g_{\rho \tau} - \partial_{\rho}g_{\mu \tau}) = \frac{1}{2}(\partial_{\tau}g_{\mu \nu} + \partial_{\mu}g_{\nu \tau} - \partial_{\nu}g_{\mu \tau})\newline = \Gamma_{\mu \tau}^{\lambda}g_{\lambda \nu}To give more clearly details for the traversible wormhole I showed in 1996 that the stress-energy tensor in a transversibel wormholes for a spin 1 field would be expressed as;
<\bar{T}_{\mu\nu}>_{ren} = <\bar{T}_{\mu\nu}>_{reg} - <\bar{T}_{\mu\nu}>_{div}where
2 \pi^2 \left( \begin{array}{c}\bar{T}_{t \tilde t} \\ \bar{T}_{\rho \tilde \rho} \\ \bar{T}_{\theta \tilde \theta} \end{array} \right)_{renormaliz} = \left( \begin{array}{l} -\frac{1}{60r_{o}^4} \ln \frac{L}{\Lambda} + \frac{1}{36}\frac{r_{o}^{\prime \prime}}{r_{o}^3} + \frac{1}{4}\frac{\Phi_{o}^{\prime \prime}}{r_{o}^2} \\ \frac{1}{60r_{o}^4} \ln \frac{L}{\Lambda} + \frac{1}{36}\frac{\Phi_{o}^{\prime \prime}}{r_{o}^2} \\ -\frac{1}{60r_{o}^4} \ln \frac{L}{\Lambda} +\frac{1}{120r_{o}^4} + \frac{1}{18}\frac{r_{o}^{\prime \prime}}{r_{o}^3} - \frac{1}{72}\frac{\Phi_{o}^{\prime \prime}}{r_{o}^2} \end{array} \right)Remember the classical Morris-Thorne conditions for a wormhole, which always imply that the tension is higher than the mass-energy.
Tension - mass = \tau - \rho_{E} = -\bar{T}_{\rho \tilde \rho} - \bar{T}_{t \tilde t} > 0And by this notation we remark that tension is larger than mass. That means the wormholes can´t exist. By inserting the result of the stress-energy tensor from my calculations. But I get the opposite;
\tau - \rho_{E} = -\frac{1}{72\pi^2 r_{o}^2}\left( 10\Phi_{o}^{\prime \prime} + \frac{r_{o}^{\prime \prime}}{r_{o}}\right) < 0Note: \Phi_{o}^{\prime \prime}>0 , r_{o}^{\prime \prime} >0
Apparently it is possibly to sent light through a wormholes, or to be more specific is it possibly to create a wormhole also to be intended for a spacecraft. I still need to make the calculations for scalar fields, but these fields are also inadequate and have some serious theoretical challenges. These serious challenges in elementary particle physic have a background in the question – “What is mass?”.
Space is made of discreste points, and I will assume space look like