Wormholes and time travel

Already Einstein (1914) worried that his theory of relativity might allow for spacetimes with so-called closed timelike curves. Gödel (1949) constructed a cosmological model where this phenomena can happen, however at the cost of an enormous amount of energy for the journey. More recently renewed interest focussed on the possibility of constructing such time machines with the help of ``wormholes.'' Wormholes are spacetimes with nontrivial topology in which a kind of tunnel exists connecting distant parts in the universe. These wormholes may not only serve as shortcuts in space but also for timetravel. Two important theorems about wormhole spacetimes are known: Hawking (1992) in his paper on ``Chronology projection conjecture'' showed, loosely speaking, that for the construction of a time machine one necessarily needs to violate the energy conditions. Friedman et al. (1993), on the other hand, proved a ``topology protection theorem'' by which it is impossible, under certain assumptions, to probe the nontrivial topology, i.e., travelling or sending light rays through the wormhole from the asymptotic region. Neither of these theorems applies to our construction: Hawking's theorem refers to spacetimes where closed causal curves exist from a certain time on (or up to a certain time), while our solution is an eternal time machine. Friedman's conclusion requires that spacetime is globally hyperbolic, a requirement which is not met by our construction. Whether or not this is physically acceptable is open. .