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Register a new userKundt geometries and memory effects in the Brans-Dicke theory of gravity
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Added by
Indranil Chakraborty
Publication date
2020
fields
Physics
and research's language is
English
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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.
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Memory effects in the exact Kundt wave spacetimes are shown to arise in the behaviour of geodesics in such spacetimes. The types of Kundt spacetimes we consider here are direct products of the form $H^2times M(1,1)$ and $S^2times M(1,1)$. Both geometries have constant scalar curvature. We consider a scenario in which initial velocities of the transverse geodesic coordinates are set to zero (before the arrival of the pulse) in a spacetime with non-vanishing background curvature. We look for changes in the separation between pairs of geodesics caused by the pulse. Any relative change observed in the position and velocity profiles of geodesics, after the burst, can be solely attributed to the wave (hence, a memory effect). For constant negative curvature, we find there is permanent change in the separation of geodesics after the pulse has departed. Thus, there is displacement memory, though no velocity memory is found. In the case of constant positive scalar curvature (Plebanski-Hacyan spacetimes), we find both displacement and velocity memory along one direction. In the other direction, a new kind of memory (which we term as frequency memory effect) is observed where the separation between the geodesics shows periodic oscillations once the pulse has left. We also carry out similar analyses for spacetimes with a non-constant scalar curvature, which may be positive or negative. The results here seem to qualitatively agree with those for constant scalar curvature, thereby suggesting a link between the nature of memory and curvature.
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