Abstract
Gravitational memory, a residual change, arises after a finite gravitational wave pulse interacts with free masses. We calculate the memory effect in massive gravity as a function of the graviton mass (m_g) and show that it is discretely different from the result of general relativity: the memory is reduced not just via the usual expected Yukawa decay but by a numerical factor which survives even in the massless limit. For the strongest existing bounds on the graviton mass, the memory is essentially wiped out for the sources located at distances above 10 Mpc. On the other hand, for the weaker bounds found in the LIGO observations, the memory is reduced to zero for distances above 0.1 Pc. Hence, we suggest that careful observations of the gravitational wave memory effect can rule out the graviton mass or significantly bound it. We also show that adding higher curvature terms reduces the memory effect.
Highlights
IntroductionThe second formulation is better because we might be able to measure the effect if that is the case
There is a very natural question that one can ask about the gravitational waves that have been detected by the LIGO/VIRGO: did the detectors leave a permanent effect on the waves or the waves left the detectors intact as they entered? one can formulate the problem in just the opposite way: did the waves leave a permanent effect on the detectors? The second formulation is better because we might be able to measure the effect if that is the case
We calculated the gravitational memory as a function of graviton mass and showed that for the graviton mass mg ≤ 10−29 eV, the memory is significantly reduced for distances beyond 1 Mpc as in the first observation of two black hole mergers which was at a distance of more than 200 Mpc
Summary
The second formulation is better because we might be able to measure the effect if that is the case It turns out, for certain gravitational waves, part of the strain can be considered as a sort of permanent effect on the detector. Since as local observers, we do not have full access to the fully consistent spacetime, it pays to see spacetime as space evolving in time, namely, to see spacetime as a history of space Such a dynamical picture requires a choice of time and other coordinates and leads to interesting phenomena and the gravitational memory is one such an event: the wave that enters the interaction with the detector masses differs in some well-defined sense from the wave that leaves the interaction. In the Appendix, we consider the massive scalar field case to set the notation and our conventions, especially how we define the sources that create the fields
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