Abstract
In this paper, we present a complete solution of Einstein’s equations for the gravitational wave (GW) problem. The full metric is taken in the usual way to be the sum of a background vacuum metric plus a perturbation metric describing the GW. The background metric used is characterized by time-varying curvature as described in a recent paper. The solution we develop here does exhibit some features found in the standard model but it also contains others that are not found in the standard model. One difference is that the solution with time-varying curvature only allows for outward-directed waves. While this might seem a minor point regarding the GW equations, it is actually a significant verification of the solution presented in our earlier paper. A more obvious difference is that the solution demands that the vacuum along with all matter must experience transverse motion with the passing of the waves. This fact leads to the idea that a new approach to the detection problem based on the Doppler effect could well be practical. Such an approach, if feasible, would be much simpler and less costly to implement than the large-scale interferometer system currently under development.
Highlights
In a recent paper [1], we proposed a new model of cosmology based on the idea that vacuum has content and serves as its own source
The effect that time-varying curvature has on gravitational waves (GW) and for this reason, it would be useful to review at least Section 8 of our original paper for the background needed to understand some of the discussion presented here
We have presented an analysis of GW in which the background metric is one with time-varying curvature
Summary
In a recent paper [1], we proposed a new model of cosmology based on the idea that vacuum has content and serves as its own source. Because the equations (but not the metric functions) must be independent of location (one point in the vacuum is exactly the same as any other point), the equations will be dependent on the spatial derivatives with respect to the coordinates ( x, y, z) but they cannot contain any explicit values of the coordinates (think of the standard wave equation) so we set those to zero which is again just evaluating the equations at the origin of each point. Since the velocity is small, we can approximate dτ ≈ dt and after changing the time coordinate to ct , we end up with, dv μ d In these equations, each chunk of the vacuum is concerned only with the connection coefficients at its location and first, because there are no spatial derivatives in (2-17) and second, because the background curvature is the same everywhere, we can immediately set x = 0. With the equations specified at least symbolically, we will turn to the source
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