Erratum: Traversable wormhole [Phys. Rev. D62, 084028 (2000)]

Abstract

In proving inequality (49) for m 2 m ; m (see the paragraph around Eq. (50)) an error is made: the term Ew 2 ÿ in fact cannot be neglected. This error invalidates the whole proof and thus the main result of the paper. So, at the moment one has to admit that there is no evidence that a static [1] macroscopic wormhole can exist without some matter more exotic than the quantized electromagnetic or scalar fields.[1] For traversable, but non-static wormholes such evidence does exist, see S. Krasnikov Phys. Rev. D 73, 084006 (2006).

Some Thoughts on Energy Conditions and Wormholes

“…(For some recent claims to the contrary, see Krasnikov [59].) Yet another misconception about QIs is that they imply that wormholes can only be slightly larger than Planck scale [13,60]. Ford and I have never claimed this.…”

Wormholes supported by polytropic phantom energy

“…In other words, its energy density takes on negative values in some suitable reference system, as does the pressure. It turns out that injecting this exotic matter into the wormhole's throat can significantly widen the radius of the throat [13].Recent interest has centered on matter that satisfies the equation of state (EoS) p = −ωρ with ω > 0. There are several possibilities: quintessence (1/3 < ω < 1), phantom energy (ω > 1), and the case ω = 1, which is equivalent to the presence of a cosmological constant.…”

“…In other words, its energy density takes on negative values in some suitable reference system, as does the pressure. It turns out that injecting this exotic matter into the wormhole's throat can significantly widen the radius of the throat [13].…”

Geometry of a centrosymmetric electric charge

“…Obtaining regular solutions to the Einstein equations with a nontrivial topology (black holes, bottlenecks, burrows, tubes, bubbles, etc.) have been made for a long time and certain advances have been made in this direction (see, for example, [6][7][8][9][10][11][12][13][14][15]). However, the general conclusion that has been drawn is distressing [6,9]: a space with a bottleneck (horn, wormhole) and two asymptotically-planar worlds can be constructed only in "pathological" cases from the standpoint of generally accepted concept of causality (negative energy density of the matter generating a gravitational field, violation of the weak energy condition [16], etc.).…”