Abstract
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat spacetime to derive gravitational forces as the gauge forces corresponding to making these symmetries local. We then consider solutions for black holes and plane gravitational waves in this approach, noting the simplicity that GA affords in both writing the solutions, and checking some of their properties. We then go on to show that a preferred gauge emerges for gravitational plane waves, in which a ‘memory effect’ corresponding to non-zero velocities left after the passage of the waves becomes clear, and the physical nature of this effect is demonstrated. In a final section we present the mathematical details of the gravitational wave treatment in GA, and link it with other approaches to exact waves in the literature. Even for those not reaching it via Geometric Algebra, we recommend that the general relativity metric-based version of the preferred gauge, the Brinkmann metric, be considered for use more widely by astrophysicists and others for the study of gravitational plane waves. These advantages are shown to extend to a treatment of joint gravitational and electromagnetic plane waves, and in a final subsection, we use the exact solutions found for particle motion in exact impulsive gravitational waves to discuss whether backward in time motion can be induced by strongly non-linear waves.
Highlights
The past three years have seen a great deal of interest in gravitational waves, with their discovery at LIGO in early 2016
To most working physicists and engineers, general relativity and gravitational waves themselves seem a very difficult and complex area—one where the mathematics is dominated by complex index manipulations and high level differential geometry, which only a few can confidently embark on and understand, and where the ‘physics’ is full of non-intuitive elements, which make the nature of the real physical predictions of the theory difficult to pin down or grasp
After a review of Geometric Algebra and Gauge Theory Gravity, we have considered gravitational waves from the point of view of these systems, and have found that a relatively simple approach and equations allow description of exact waves from general relativity
Summary
The past three years have seen a great deal of interest in gravitational waves, with their discovery at LIGO in early 2016. By formulating general relativity as a gauge theory (similar to those of the strong and weak interactions) in flat space, written using the mathematics of GA, the theory and the nature of its physical predictions become much clearer This will be illustrated by the case of gravitational waves themselves, where the GA approach suggests a new ‘gauge’ in which to study their physics, which has immediate and appealing links to electromagnetism, and which helps to iron out various misunderstandings and problems with gravitational waves and their detection which have surfaced before. Geometric Algebra, Gravity and Gravitational Waves Page 3 of 41 79 observation and for their theoretical relevance considered This discussion is mainly in the nature of a review, rather than giving detailed mathematical derivations, but in the final sections of this article we fill in many of the details, so that the nature of the new gauge and solutions can be clearly seen. We should note for those readers interested primarily in the particular ‘memory effect’ for gravitational waves discussed here, that this has been independently discovered, at about the same time as the work reported here, and related to the Brinkmann metric, by Gary Gibbons, Peter Horvathy and co-workers, and that the paper [28] would be good to consult on this, being the first in a series of papers by them on this topic
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
