9.0 - Changes in Curvature of Spacetime

This chapter just covers the last base for details. Einstein calculated a curvature in space for every gravitational field. For all regular stars, the change is extremely small, less than a light second. However, if we are talking about major galactic distances, it is possible that there would be a noticable curvature caused by the center of the galaxy, or some unknown localized curvatures, which could have some effect on the SGC measurements. I left this chapter to the end, because, these type of measurements are undoubtably the furthest away in the future. We are about as close to zooming across the galaxy where these effects might matter as the bow and arrow is distant in development from the space shuttle.

The SGC system is set with four coordinates to track changes in a theoretically flat spacetime. Curvatures in spacetime resulting from gravitational fields are not compensated for using only four coordinates. If such accuracy is desired, a fifth "Spacetime Curvature" (SC) coordinate may be added.

 The nature of such a SC coordinate may be defined as;

  1. A first order spacetime curvature resulting from a gravitational field.
  2. A second order - larger localized spacetime curvature.
  3. A third order general spacetime curvature that applies to large areas of galactic scale.
Examining the three possibilities in more detail shows that in the first case, a spacetime curvature resulting from a gravitational field, is an accepted value defined in Einstein's Special Theory of Relativity. Such a curvature is geometric and flattens out based on the square of the distance from the surface of the mass. A SC coordinate defining a curvature of the first order would follow any massive object, such as a star, and dissipate in strength of spacetime curvature further away from the star. A first order curvature would not amount to a large enough change in distance on an interstellar scale unless the mass is sufficiently large, such as a black hole. For all other masses, the change in distance caused by such a spacetime curvature would be minute even on a planetary scale.

 In the second case, there is, to date, no evidence of localized spacetime curvature. It is therefore impossible at this time to state if such theorized second order curvatures would be sufficiently large enough to need inclusion in a galactic coordinate system.

 In the third case, it is generally accepted that there may be a large black hole in the center of the galaxy. The black hole plus the combined mass of the galactic central area would certainly alter galactic distances in a subtle way, growing weaker, the further one is distanced from the center of the galaxy. Such a third order curvature of spacetime would affect the distances in a long galactic trip and may need to be factored in using the fifth SC coordinate, much in a similar way to the north pole magnetic deviation experienced on Earth.

 In conclusion, all of the above deviations are well below the accuracy range of our current knowledge of interstellar distances. In other words, before it becomes necessary to use a fifth SC coordinate, one must first vastly improve the accuracy of current measurements. A SC coordinate may have it's place in an improved SGC map that has been surveyed for accuracy in the future.

Forward to the Appendix

Backward to Chapter 8 - Relativistic Changes

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