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Register a new userSoft Gravitons & the Memory Effect for Plane Gravitational Waves
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The gravitational memory effect due to an exact plane wave provides us with an elementary description of the diffeomorphisms associated with soft gravitons. It is explained how the presence of the latter may be detected by observing the motion of freely falling particles or other forms of gravitational wave detection. Numerical calculations confirm the relevance of the first, second and third time integrals of the Riemann tensor pointed out earlier. Solutions for various profiles are constructed. It is also shown how to extend our treatment to Einstein-Maxwell plane waves and a midi-superspace quantization is given.
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We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einsteins vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zeldovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the velocity memory effect, considered by Braginsky, Thorne, Grishchuk, and Polnarev.
Circularly polarized gravitational sandwich waves exhibit, as do their linearly polarized counterparts, the Velocity Memory Effect: freely falling test particles in the flat after-zone fly apart along straight lines with constant velocity. In the inside zone their trajectories combine oscillatory and rotational motions in a complicated way. For circularly polarized periodic gravitational waves some trajectories remain bounded, while others spiral outward. These waves admit an additional screw isometry beyond the usual five. The consequences of this extra symmetry are explored.
The Eisenhart lift of a Paul Trap used to store ions in molecular physics is a linearly polarized periodic gravitational wave. A modified version of Dehmelts Penning Trap is in turn related to circularly polarized periodic gravitational waves, sought for in inflationary models. Similar equations rule also the Lagrange points in Celestial Mechanics. The explanation is provided by anisotropic oscillators.
We include the single graviton loop contribution to the linearized Einstein equation. Explicit results are obtained for one loop corrections to the propagation of gravitational radiation. Although suppressed by a minuscule loop-counting parameter, these corrections are enhanced by the square of the number of inflationary e-foldings. One consequence is that perturbation theory breaks down for a very long epoch of primordial inflation. Another consequence is that the one loop correction to the tensor power spectrum might be observable, in the far future, after the full development of 21cm cosmology.
General metric theories in a four-dimensional spacetime allow at most six polarization states (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). If a sky location of a GW source with the electromagnetic counterpart satisfies a single equation that we propose in this paper, both the spin-1 modes and spin-2 ones can be eliminated from a certain combination of strain outputs at four ground-based GW interferometers (e.g. a network of aLIGO-Hanford, aLIGO-Livingston, Virgo and KAGRA), where this equation describes curves on the celestial sphere. This means that, if a GW source is found in the curve (or its neighborhood practically), a direct test of scalar (spin-0) modes separately from the other (vector and tensor) modes become possible in principle. The possibility of such a direct test is thus higher than an earlier expectation (Hagihara et al. PRD, 100, 064010, 2019), in which they argued that the vector modes could not be completely eliminated. We discuss also that adding the planned LIGO-India detector as a fifth detector will increase the feasibility of scalar polarization tests.
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