Simulations of space–times that contain negative energies can help us to better understand wormholes or the interior of black holes. For now, however, the physicists who performed the new study, who admit to being big fans of Star Trek, have used their result to model the gravitational waves that would be emitted by a hypothetical failing warp drive.
Gravitational waves, which are ripples in the fabric of space–time, are emitted by cataclysmic events in the universe, like binary black hole and neutron star mergers. They might also be emitted by more exotic space–times such as wormholes or warp drives, which unlike black hole and neutron mergers, are still the stuff of science fiction.
First predicted by Albert Einstein in his general theory of relativity, gravitational waves were observed directly in 2015 by the Advanced LIGO detectors, which are laser interferometers comprising pairs of several-kilometre-long arms positioned at right angles to each other. As a gravitational wave passes through the detector, it slightly expands one arm while contracting the other. This creates a series of oscillations in the lengths of the arms that can be recorded as interference pattern variations.
The first detection by LIGO arose from the collision and merging of two black holes. These observations heralded the start of the era of gravitational-wave astronomy and viewing extreme gravitational events across the entire visible universe. Since then, astrophysicists have been asking themselves if signals from other strongly distorted regions of space–time could be seen in the future, beyond the compact binary mergers already detected.
Warp drives or bubbles
A “warp drive” (or “warp bubble”) is a hypothetical device that could allow space travellers to traverse space at faster-than-light speeds – as measured by some distant observer. Such a bubble contracts spacetime in front of it and expands spacetime behind it. It can do this, in theory, because unlike objects within space–time, space–time itself can bend, expand or contract at any speed. A spacecraft contained in such a drive could therefore arrive at its destination faster than light would in normal space without breaking Einstein’s cosmic speed limit.
The idea of warp drives is not new. They were first proposed in 1994 by the Mexican physicist Miguel Alcubierre who named them after the mode of travel used in the sci-fi series Star Trek. We are not likely to see such drives anytime soon, however, since the only way to produce them is by generating vast amounts of negative energy – perhaps by using some sort of undiscovered exotic matter.
A warp drive that is functioning normally, and travelling at a constant velocity, does not emit any gravitational waves. When it collapses, accelerates or decelerates, however, this should generate gravitational waves.
A team of physicists from Queen Mary University of London (QMUL), the University of Potsdam, the Max Planck Institute (MPI) for Gravitational Physics in Potsdam and Cardiff University decided to study the case of a collapsing warp drive. The warp drive is interesting, say the researchers, since it uses gravitational distortion of spacetime to propel a spaceship forward, rather than a usual kind of fuel/reaction system.
Decomposing spacetime
The team, led by Katy Clough of QMUL, Tim Dietrich from Potsdam and Sebastian Khan at Cardiff, began by describing the initial bubble by the original Alcubierre definition and gave it a fixed wall thickness. They then developed a formalism to describe the warp fluid and how it evolved. They varied its initial velocity at the point of collapse (which is related to the amplitude of the warp bubble). Finally, they analysed the resulting gravitational-wave signatures and quantified the radiation of energy from the space–time region.
While Einstein’s equations of general relativity treat space and time on an equal footing, we have to split the time and space dimensions to do a proper simulation of how the system evolves, explains Dietrich. This approach is normally referred to as the 3+1 decomposition of spacetime. “We followed this very common approach, which is routinely used to study binary black hole or binary neutron star mergers.”
It was not that simple, however: “given the particular spacetime that we were investigating, we also had to determine additional equations for the simulation of the material that is sustaining the warp bubble from collapse,” says Dietrich. “We also had to find a way to introduce the collapse that then triggers the emission of gravitational waves.”
Since they were solving Einstein’s field equation directly, the researchers say they could read off how spacetime evolves and the gravitational waves emitted from their simulation.
Very speculative work
Dietrich says that he and his colleagues are big Star Trek fans and that the idea for the project, which they detail in The Open Journal of Astrophysics, came to them a few years ago in Göttingen in Germany, where Clough was doing her postdoc. “Sebastian then had the idea of using the simulations that we normally use to help detect black holes to look for signatures of the Alcubierre warp drive metric,” recalls Dietrich. “We thought it would be a quick project, but it turned out to be much harder than we expected.”
The researchers found that, for warp ships around a kilometre in size, the gravitational waves emitted are of a high frequency and, therefore, not detectable with current gravitational-wave detectors. “While there are proposals for new gravitational-wave detectors at higher frequencies, our work is very speculative, and so it probably wouldn’t be sufficient to motivate anyone to build anything,” says Dietrich. “It does have a number of theoretical implications for our understanding of exotic spacetimes though,” he adds. “Since this is one of the few cases in which consistent simulations have been performed for spacetimes containing exotic forms of matter, namely negative energy, our work could be extended to also study wormholes, the inside of black holes, or the very early stages of the universe, where negative energy might prevent the formation of singularities.
Even though they “had a lot of fun” during this proof-of-principle project, the researchers say that they will now probably go back to their “normal” work, namely the study of compact binary systems.
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