Hideki Maeda presented a simple traversable wormhole solution which violate energy conditions only at the planck scale
Wormhole is a configuration of spacetimes containing distinct non-timelike infinities. In particular, a wormhole that contains a casual curve connecting such infinities are referred to as a traversable wormhole. Several examples of traversable wormholes have been already discussed by us in our articles. Now, Hideki Maeda presented a simple static spacetime which describes a spherically symmetric traversable worm-hole characterized by a length parameter, l and reduces to Minkowski in the limit l → 0. His findings recently appeared in Arxiv.
He showed that, this wormhole connects two distinct asymptotically flat regions with vanishing ADM mass and the areal radius of its throat is exactly l. Additionally, all the standard energy conditions i.e. null-energy condition, weak energy condition, dominant energy condition and standard energy condition are violated outside the proper radial distance approximately 1.60 l from the wormhole throat.
Finally, he computed the total amount of negative energy required to support this wormhole and found that, if l is identified as the Planck length lp (≃ 1.616 × 10¯35 m), the total amount of the negative energy supporting this wormhole is only E ≃ −2.65 mpc², which is the rest mass energy of about – 5.77 × 10¯5 g. For a “humanly traversable” wormhole with l = 1m, he obtained mass of −3.57 × 1027 kg, which is about –1.88 times as large as Jupiter’s mass.
“Ofcourse, an important task is to identify a theory of gravity which admits the static spacetime as a solution. Once such theory is identified, a subsequent task is to study the stability. Since the region of the NEC violation is tiny, our wormhole could be a dynamically stable configuration in the semiclassical regime. These important tasks are left for future investigations.”— he concluded.
Reference: Hideki Maeda, “A simple traversable wormhole violating energy conditions only at the Planck scale”, Arxiv, pp. 1-4, 2021.
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