Abstract
Memory effects are studied in the simplest scalar–tensor theory, the Brans–Dicke (BD) theory. To this end, we introduce, in BD theory, novel Kundt spacetimes (without and with gyratonic terms), which serve as backgrounds for the ensuing analysis on memory. The BD parameter omega and the scalar field (phi ) profile, expectedly, distinguishes between different solutions. Choosing specific localised forms for the free metric functions H'(u) (related to the wave profile) and J(u) (the gyraton) we obtain displacement memory effects using both geodesics and geodesic deviation. An interesting and easy-to-understand exactly solvable case arises when omega =-2 (with J(u) absent) which we discuss in detail. For other omega (in the presence of J or without), numerically obtained geodesics lead to results on displacement memory which appear to match qualitatively with those found from a deviation analysis. Thus, the issue of how memory effects in BD theory may arise and also differ from their GR counterparts, is now partially addressed, at least theoretically, within the context of this new class of Kundt geometries.
Highlights
The detection of gravitational waves in binary mergers has opened up new prospects for testing theories of gravity in the strong field regime [1,2]
Thereafter, we study geodesics and geodesic deviation to infer about memory effects
We find increasing separation between the geodesics after the departure of the pulse. This is in sharp contrast to the profiles obtained in GR. In the latter theory we found from geodesic analysis that positive curvature scenarios give rise to a frequency memory effect [46]
Summary
The detection of gravitational waves in binary mergers has opened up new prospects for testing theories of gravity in the strong field regime [1,2]. In [19], the authors have showed how to isolate the gravitational wave contribution from the background spacetime by resorting to Fermi normal coordinates and solving the geodesic deviation equation. The coordinate system is locally Minkowskian and the notion of displacement and velocity memory effect is qualitatively similar to exact plane wave spacetimes [15,47,48]. In such Fermi coordinates, we construct parallely transported tetrads along a given timelike geodesic. Relevant mathematical formulae used in the paper are listed in an Appendix
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