Refraction of geodesics by impulsive spherical gravitational waves in constant-curvature spacetimes with a cosmological constant

Abstract

We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in a Minkowski, a de Sitter, or an anti-de Sitter universe. Using the continuous form of these metrics we derive explicit junction conditions and simple refraction formulas for null, timelike, and spacelike geodesics crossing a general impulse of this type. In particular, we present a detailed geometrical description of the motion of test particles in a special class of axially symmetric spacetimes in which the impulse is generated by a snapped cosmic string.

Superboost transitions, refraction memory and super-Lorentz charge algebra

“…We also would like to point out that there is a non-linear displacement memory induced by a superboost transition, when it is accompanied by a supertranslation transition. This case was not considered in [42][43][44] where all supertranslation transitions were vanishing. In order to describe the effect, we can consider either timelike or null geodesics.…”

Memory effect and BMS-like symmetries for impulsive gravitational waves

“…Here, we use a local coordinate system in which the metric tensor is continuous but its first derivative has discontinuity across the history of the signal and include a thin null-shell along with the wave signal. There are rigorous results reported in exact IGW spacetimes describing the existence, uniqueness and generic properties of geodesics across a null impulsive surface [39,40,41]. However our approach is somewhat different.…”

Asymptotic Symmetries in the Gauge fixing Approach and the BMS group

“…The analogous memory effects can also be established in electrodynamics (electromagnetic memory effect) [149,150] and in Yang-Mills theory (color memory effect) [148] where a field is turned on as a result of a burst of energy passing through the region of interest, leading to an observable phenomenon. Notice that other memory effects have been identified in gravity [69,[151][152][153][154][155][156][157], including the spin memory effect and the refraction memory effect. We now briefly discuss the relation between these different topics.…”