A region-delimited gravitational wave field can be constructed, such that a subset of geodesics crossing this region will move faster than nearby geodesics moving entirely inside flat spacetime, along a preferred direction. Null geodesics inside this region will move faster-than-light according to far away observers. The waveform is synthesized from homogeneous plane wave solutions, and the resulting field is the gravitational equivalent of a Gaussian beam.
Several authors have proposed mechanisms within the standard theory of General Relativity (GR) to allow some level of circumvention around the light speed limit, by warping the spacetime geometry in some compact region. However, all the mechanisms proposed so far require the engineered spacetime region to be filled with matter that violates well established energy conditions, and is not known to exist in nature. But even ignoring the problem of violation of the energy conditions, these geometries have other problems related to acausal setup of the exotic matter distribution, as well as quantum instabilities in the semiclassical limit
However, the idea of using matter to curve surrounding spacetime does not exhaust the possibilities that GR offers in order to create customized geometries. Gravitational waves (GW) are themselves perturbations of geometry that travel at the speed of light. Even while the full theory of GR is a nonlinear theory, the principle of superposition still applies within the limit of weak plane waves, and one can consider some superpositions of such planar waves physically valid perturbations. The present work shows that for specially crafted gravitational waveforms of this type, one can produce geometries in pure vacuum with Faster-Than-Light (FTL) properties, similar to those obtained via other geometrical drives.
In this work, the geometry of null congruences can be affected in a way that allows FTL communication. To be precise, we construct a focal region of a gravitational waveform composed of traceless and transverse planar waves, and find that null congruences entering the focal region can become asymptotically accelerated, such that they arrive effectively before similar geodesics that do not enter the field region, according to distant observers. The asymptotic delay or advancement of congruences will be affected by the local phase of the perturbation at the moment the geodesic enters the region, the period of the oscillation, as well as the width of the focal region.
Given the complex nonlinear geodesic equations that result from the Gaussian perturbation, we were only able to compute analytically the first order correction to the geodesic null and time-like rays crossing the field, and its derivation is detailed
We have established that within GR, certain gravitational waveforms can result in geodesics that arrive at distant points earlier than light signals in flat spacetime. We presented an example waveform that can be used to manifest FTL behavior, and obtained an analytic first order perturbative approximation of geodesics approaching the field region. We notice that the timing of entrance to the field region determines the asymptotic delay or advance of signals. The optimal shortcut geodesics are those that cross the field region as close as possible to the time and position of the minimum of the metric waveform.
Compared to other FTL schemes like the Alcubierre drive or Lorentzian wormholes, which rely on unphysical matter fields to stabilize the geometry, the current approach relies only on gravitational wave generation and transmission through empty space. Assuming the daunting problem of astronomical scale gravitational wave generation is somehow solved, this method could in principle enable FTL travel without appealing to exotic physics. However a detailed analysis of tidal forces is required before assessing the feasibility of this scheme for transit of payloads.
The nature of the shortcut generation involves the creation of waveforms that compress and dilate spacetime in the direction of flight. In order for signals (or ships) to be able to take advantage of the metric-contracting fields, they must carefully control their timing synchronization, in order to cross the field regions as close as possible to the compression valley, where the distance is minimal between opposing sides of the field region. The region must be crossed in substantially less than T /2, with T being the period of the gravitational wave. Even if the compression of each field region is small, large distance reduction could be accomplished by bridging many pre-configured field regions in a timely manner. It is conceivable that other field configurations exist that achieve better distance compression patterns. Even without exploiting the FTL aspects of the field, time-like geodesics can still be substantially accelerated or decelerated with special field configurations of this type, while remaining in free fall during the transit.
Due to the transversal nature of gravitational waves, the gravitational sources must be distributed orthogonally to the direction of desired FTL geodesic path. These gravitational beams have to be precisely oriented and timed decades in advance, as gravitational waves propagate at the speed of light. This implies some sort of deployment of a wide scale network of gravitational generators around entire star clusters. This presents an unfathomably hard logistic and technological problem. Perhaps, some future Type-III civilization, millions of years in the future, might manage to address them.
Arxiv – Creating spacetime shortcuts with gravitational waveforms, Charles Quarra Charles is a physicist and software developer Charles J. Quarra. He has spoken at Icarus Interstellar conferences and works with the Icarus Interstellar projects.