Geodesics in exact plane wave spacetimes and the memory effect
Year: 2019
Type: preprint
Abstract: Recently, in several articles [notably, Phys. Rev. D 96, 064013(2017)], ithas been shown qualitatively, how the displacement and velocity memory effects
can be analysed by studying geodesics in the exact, vacuum, plane gravitational
wave line element. In particular, one may look for such memory effects by
investigating the behaviour of geodesics using the geodesic equations
themselves, the geodesic deviation equations or the Raychaudhuri equations for
geodesic congruences. In our work here, we first demonstrate qualitatively,
using geodesic deviation, how a memory effect may arise. Thereafter, we solve
the geodesic equations explicitly to provide simple and largely analytical
examples of such effects, using two different pulse profiles in the exact plane
gravitational wave line element: (a) a square pulse and (b) a sech-squared
pulse. We show the emergence of displacement and velocity memory effects for
timelike geodesics, for each of the above-mentioned profiles. Finally, we
demonstrate in qualitative terms, how the Raychaudhuri equations may be used to
arrive at memory effects through the nature of the shear and expansion of
geodesic congruences. As an illustration, we obtain the shear and expansion for
timelike geodesic congruences in this line element, for the two pulse profiles
mentioned earlier. The growth of shear in causing a focusing of an initially
parallel congruence, after the pulse has left, is seen to be distinctly linked
to the memory effect.
Source: arXiv (Cornell University)
Authors: Indranil Chakraborty, Sayan Kar
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2914965402