What would for an observer be the mass of an isolated wormhole (meaning that there is no gas and no mass of stars around it) if the wormhole mouth opposite to the observer reflects the light of a region from the galaxy it opens into.

Wormholes per definition require negative energy in the form of exotic matter so as to have their mouths open. Would this negative mass be the only mass of the wormhole object or for an observer in the isolated wormhole also include the light reflected of stars and gases visible through the wormhole of another galaxy.

Wormholes connect two systems for only a short time, and collapse when too much time has passed, or too much mass has passed through them. My question would be for wormholes that can have their mouths connected either naturally or artificially for a reasonable length of time.

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    $\begingroup$ This is a qood question, initially I would have believed that it would take the apparent mass based on distance from and size of mass on the opposite side of the wormhole. This would be similar to how much light gets through a hole on a piece of paper. However the negative energy piece I have not thought of. I know this doesn't help. I just really like the question. $\endgroup$ – Joe Jan 30 '15 at 12:43
  • $\begingroup$ Some papers, and this suggest that the dacay mode of the energy through a gravitational wave might be influenced from the local geometry(metric). The object might be a star, black hole, wormhole, ...etc even not having a spherical symmetry. $\endgroup$ – Nikey Mike Jan 17 '16 at 23:27
  • $\begingroup$ Is the wormhole asymptotically flat and stationary? Then it has a Komar or ADM mass like anything else does. Otherwise, it's nontrivial how to define the notion of mass. $\endgroup$ – alexarvanitakis Feb 15 at 21:59

I found a post here on physicsforums.com which has some useful links in the post by "pervect". One is to this article by physicist John Cramer, saying that each time a mass M passes through a wormhole mouth, "the entrance mouth has its mass increased by M, and the exit mouth has its mass reduced by an amount -M", and that this can eventually cause one of the mouths to have a net negative mass. Presumably light passing through a wormhole could have the same effect, based on mass-energy equivalence in general relativity. Pervect notes that in this context the "mass" being discussed is the ADM mass, and links to this post discussing the technical details of calculating the ADM mass of wormhole mouths, as well as some issues relating to quantum uncertainty in mass--I don't know enough general relativity to follow the technical details here, but the author seems to say that the mass of a mouth cannot actually become negative, perhaps for reasons relating to the "quantum inequalities" postulated to restrict negative energy that are discussed in this article. (maybe when John Cramer talked about the mass becoming negative he was giving the answer in "pure" general relativity without considering quantum physics?) Hopefully someone else who understands these topics better will weigh in, but I thought these links would be useful as pointers to research that would likely be relevant to answering your question.

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  • $\begingroup$ As per your answer the mass will be related to the matter within the tube of the wormhole and the difference of the mass located in the mouths of both ends one negative and another positive as you sugested. So I guess the lenght of the tube is then important as well as the length of time it remains open $\endgroup$ – Barnaby Jan 31 '15 at 2:34
  • $\begingroup$ @Barnaby - I don't know if it's correct that the mass has anything to do with matter inside the tube, after all a black hole is a "vacuum solution" but it does have mass, similarly with gravitational waves--in general relativity a region of curved spacetime can have mass even if there is no matter field present. A traversable wormhole does require at least a thin layer of negative mass/energy to hold it open, but it may be that this does not account for its mass. $\endgroup$ – Hypnosifl Jan 31 '15 at 4:03

A wormhole solution necessarily violates the averaged null energy condition (ANEC). The positive energy theorem says that if the dominant energy condition (DEC) holds, then the ADM mass is strictly greater than zero for a non-flat spacetime. The DEC is stronger than the ANEC. So a wormhole must violate the DEC, and therefore the positive energy theorem doesn't apply, and there seems to be no conclusive answer as to the sign of the wormhole's ADM mass. It's of course possible that there is some other argument that I'm not aware of that would give a more definite answer about the sign of the mass.

Kip Thorne's group at Cal Tech did a lot of work on wormholes and CTCs in the 1980's. Some of their papers, as far as I recall, seemed to implicitly assume a positive ADM mass. They describe a mechanism by which any wormhole can always be made into an eternal time machine. This is briefly described, e.g., in Echeverria 1991, and their mechanism basically involves accelerating one mouth so that it has some cumulative time dilation. Reading those arguments, my understanding was always that that they were talking about manipulating the mouth by attracting it gravitationally with an external positive mass. But of course if the mouth had a negative mass, you could manipulate it just as easily using the repulsion of a positive mass. It might be helpful to comb through some of those old papers and see if they ever explicitly give some reason why the ADM mass should have a particular sign.

Echeverria 1991 - Echeverria, 1991, "Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory," http://authors.library.caltech.edu/6469/

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