Abstract
Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ‘spacetime’. His general theory of relativity further taught us that spacetime is not just a stage on which dynamics takes place, but is a participant: the field equation of general relativity connects matter dynamics to the curvature of spacetime. Curvature is responsible for gravity, carrying us beyond the Newtonian conception of gravity that had been in place for the previous two and a half centuries. Much research in gravitation since then has explored and clarified the consequences of this revolution; the notion of dynamical spacetime is now firmly established in the toolkit of modern physics. Indeed, this notion is so well established that we may now contemplate using spacetime as a tool for other sciences. One aspect of dynamical spacetime—its radiative character, ‘gravitational radiation’—will inaugurate entirely new techniques for observing violent astrophysical processes. Over the next 100 years, much of this subject's excitement will come from learning how to exploit spacetime as a tool for astronomy. This paper is intended as a tutorial in the basics of gravitational radiation physics.
Highlights
Despite his intention to stick only with that which can be observed, Newton described space and time using exactly the abstract notions that he otherwise deplored [3]: Absolute space, in its own nature, without relation to anything external, remains always similar and immovable
Special relativity put an end to these abstractions: time is nothing more than that which is measured by clocks, and space is that which is measured by rulers
Ten years after his paper on special relativity, Einstein endowed spacetime with curvature and made it dynamical [5]. This provided a covariant theory of gravity [6], in which all predictions for physical measurements are invariant under changes in coordinates
Summary
As GW detectors have improved and approached maturity, many papers have been written reviewing this field and its promise. When we discuss linearized theory, we will sometimes be sloppy and sum over adjacent spatial indices in the same position. (As we will discuss, this is allowable because, in linearized theory, the position of a spatial index is immaterial in Cartesian coordinates.) A quantity that is symmetrized on pairs of indices is written as. We demonstrate that the linearized Einstein equations can be written as five Poisson-type equations for certain combinations of the spacetime metric, plus a wave equation for the transverse-traceless components of the metric perturbation. This analysis helps to clarify which degrees of freedom in general relativity are radiative and which are not, a useful exercise for understanding spacetime dynamics. We conclude by discussing very briefly some topics that we could not cover in this paper, with pointers to good reviews
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