Abstract
The metrics of general relativity generally fall into two categories: those which are solutions of the Einstein equations for a given source energy-momentum tensor and the “reverse engineered” metrics—metrics bespoke for a certain purpose. Their energy-momentum tensors are then calculated by inserting these into the Einstein equations. This latter approach has found frequent use when confronted with creative input from fiction, wormholes and warp drives being the most famous examples. In this paper, we again take inspiration from fiction and see what general relativity can tell us about the possibility of a gravitationally induced tractor beam. We base our construction on warp drives and show how versatile this ansatz alone proves to be. Not only can we easily find tractor beams (attracting objects), but repulsor/pressor beams are just as attainable, and a generalization to “stressor” beams is seen to present itself quite naturally. We show that all of these metrics would violate various energy conditions. This provides an opportunity to ruminate on the meaning of energy conditions as such and what we can learn about whether an arbitrarily advanced civilization might have access to such beams.
Highlights
Within the context of standard general relativity, there has been over 33 years of serious theoretical work on the possibility of “traversable wormholes” [1,2,3,4,5], 29 years of recent work on “time machines” [6,7,8,9,10,11,12] and over 27 years of work on the theoretical possibility of “warp drives” [13,14,15,16,17,18]
We show how to analyze tractor/pressor/stressor beams within the framework of standard general relativity
The analysis was made based on modified warp drive spacetimes, by creating a “beam-like” profile
Summary
Within the context of standard general relativity, there has been over 33 years of serious theoretical work on the possibility of “traversable wormholes” [1,2,3,4,5], 29 years of recent work on “time machines” [6,7,8,9,10,11,12] and over 27 years of work on the theoretical possibility of “warp drives” [13,14,15,16,17,18]. As always, when working in this area of speculative physics, including wormholes, warp drives and tractor/pressor/stressor beams, a major justification for undertaking this exercise is to push general relativity to the breaking point, in the hope that the resulting wreckage will tell us something interesting—possibly even about quantum gravity [5,16]. A recurring theme in the analysis is the use of the classical point-wise energy conditions (null, weak, strong and dominant, abbreviated NEC, WEC, SEC and DEC, respectively) [32,33,34,35] They can be considered as an attempt to remain as agnostic as possible about underlying equations of state. Significant parts of these papers are incorrect, misguided and/or misleading (see [18] for details)
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